# List of publications of Prof. Tim Porter

Name
Prof. Tim Porter
Position
Emeritus Professor
Email
t.porter@bangor.ac.uk
Phone
Location

## Books

• (with J.-M.Cordier), Shape Theory: Categorical Methods of Approximation, Mathematics and its Applications, Ellis Horwood Ltd., March 1989, 207 pages. Dover addition (to appear 2008)
• (with N.D.Gilbert), Knots and Surfaces, textbook, Oxford University Press, November 1994, 268 pages.
• (with K.H. Kamps), Abstract Homotopy and Simple Homotopy Theory, World Scientific, 462pp (ISBN 981-02-1602-5) June 1997.A copy of the Mathematical Review of the book is available here.
• Mathematics and Knots'', booklet accompanying the exhibition of the same name (see below), Bangor, 1989, 27 pages.
Commissioned Sections of Books
• Proper Homotopy Theory'', 40 pages (invited chapter in the Handbook on Algebraic Topology, Ed. I.M.James, Elsevier,1995).

## Exhibition and Related Material

• (with the Mathematics and Knots'' team: R.Brown, N.D.Gilbert, T.Porter.) 16 A2 boards in the Mathematics and Knots'' exhibition, Bangor, 1989, also available on the Web at http://www.bangor.ac.uk/ma/CPM/exhibit/welcome.htm.

## Conference Proceedings

• Proceedings of the International Category Theory Meeting, 1989, Bangor, in Cahiers de Topologie et Géom. Diff. Cat., 32, 1991, First two and a half issues, approximately 240 pages.

## Translations

• (with M.-C. Porter) Yves Diers, Categories of Boolean Sheaves of Simple Algebras, Springer, Lecture Notes in Math. No. 1187, 1986 (from original French manuscript).

## Research Papers

(Unless otherwise indicated the author is Porter, T.''. All are refereed articles.)

### Mathematics

• Sur le théorème de Van Kampen et la construction de Vietoris, C. R. Acad. Sc. Paris, Série A, t. 274, 1972, pp. 392-394.
• Sur le type simple d'homotopie des groupoïdes, C. R. Acad. Sc. Paris, Série A, t.275, 1972, pp. 381-383.
• Sur le type simple d'homotopie d'un groupoïde semifini, C. R. Acad. Sc. Paris, Série A, t.275, 1972, pp. 629-631.
• Sur le type d'homotopie couplé, C. R. Acad. Sc. Paris, Série A, t.276, 1973, pp. 985-987.
• Cech homotopy I, Jour. London Math. Soc., 1, 6, 1973, pp. 429-436.
• Cech homotopy II, Jour. London Math. Soc., 2, 6, 1973, pp. 667-675.
• Le produit des espaces compacts dans la categorie, Vtop, C. R. Acad. Sc. Paris, Série A, t.277, 1973, pp. 331-332.
• Des connexions entre la théorie de la forme et la théorie des semicomplexes, C. R. Acad. Sc. Paris, Série A, t.277, 1973, pp. 357-358.
• Borsuk's theory of shape and Cech homotopy, Math. Scand., 33, 1973, pp. 83-89.
• A Cech-Hurewicz isomorphism theorem for movable metric compacta, Math. Scand., 33, 1973, pp. 90-96.
• Obstructions in Shape Theory, Bull. Amer. Math. Soc., 79, 1973, pp. 1206-1209.
• Formules generalisées de récurrence et foncteur premier dérivé de lim, C. R. Acad. Sc. Paris, Série A t.277, 1973, pp. 977-978.
• Generalised Shape Theory, Proc. Royal Irish Acad. 74, Section A, 1974, pp. 33-48.
• The first derived equaliser of a pair of abelian group homomorphisms, Proc. Amer. Math. Soc., 42, 1974, pp. 77-80.
• Cech Homotopy III, Bull. London Math. Soc., 6, 1974, pp. 207-311.
• On the T -shape of the suspension of a space, Bull. Acad. Polon. Sci., Sér. Sci., math., ast. et phys., XXII, 1974, pp. 847-850.
• Paired homotopy type, Proc. Royal Irish Acad. 74, Section A, 1974, pp. 103-113.
• Stability Results for Topological Spaces, Math. Zeit. 150, 1974, pp. 1-21.
• Une théorie des obstructions dans une catégorie des diagrammes et des applications à la théorie d'homotopie de Cech I, Ann. Soc. Sci. Bruxelles, t88, 1974, pp. 281-291.
• Porter, T. and Seda, A.K.: Une application de la théorie des Obstructions équivariantes à la théorie des espaces fibrés, C. R. Acad. Sc. Paris, Série A, t.278, 1974, pp. 745-746.
• Une théorie des obstructions ...II, Ann. Soc. Sci. Bruxelles, t.89, 1975, pp. 25-40.
• Une théorie des obstructions ... III, Ann. Soc. Sci. Bruxelles, t.89, 1975, pp. 375-384.
• Une théorie des obstructions ...IV, Ann. Soc. Sci. Bruxelles, t.90, 1976, pp. 77-87.
• Stability of Algebraic Inverse Systems, II, Purity and Localization, Jour. Pure Applied Alg., 7, 1976, pp. 133-143.
• Stability Results for Algebraic Inverse Systems, Proc. Royal Irish Acad,, 76, 1976, Section A, pp. 79-83.
• Une théorie des obstructions ... V, Ann. Soc. Sci. Bruxelles, t.90, 1976, pp. 173-181.
• Categories of promodules (Colloque sur la théorie et applications des catégories - Amiens 1975), Cahiers Top. Géom. Diff., 16. (1976), pp. 295-300.
• Abstract homotopy theory in procategories, Cahiers Top. Géom. Diff., 17, 1976, pp. 113-124.
• Torsion theoretic results in procategories I, II, III, Proc. Royal Irish Acad. 76 (1976) Section A, pp. 145-154, 155-164 and 165-172.
• Quelques localisations dans les catégories pro-Grothendieck, C. R. Acad. Sc. Paris, t.283 (1976) pp. 567-569.
• Quelques résultats sur les anneaux semi-Nöetheriens, Bull. Acad. Polon. Sci., Sér. Sci., Math., astr. et phys., XXIV, 1976, pp. 829-834.
• Coherent prohomotopical algebra, Cahiers Top.Géom.Diff., 18, (1978) pp. 139-179.
• Coherent prohomotopy theory, Cahiers Top. Géom. Diff., 19, (1978) pp. 3-46.
• Stability of Algebraic Inverse Systems I: Stability, weak stability and the weakly stable socle. Fund. Math. 100 (1978) pp. 17-33.
• Essential properties of pro-objects in Grothendieck categories, Cahiers Top. Géom. Diff., 20 (1979) pp. 3-57.
• Une théorie catégorique d'homotopie simple, Cahiers Top. Géom. Diff. 22, (1981) pp. 191-199.
• Cech and Steenrod homotopy and the Quigley exact couple in strong shape and proper homotopy theory, Jour. Pure Applied Alg., 24 (1982) pp. 303-312.
• Reduced Powers, Ultra Powers and Exactness of Limits, Jour. Pure Applied Alg., 26 (1982) pp. 325-330.
• Internal Categories and Crossed Modules, Proc. Inter. Conf. of Category Theory, Gummersbach, 1981, in Springer Lecture Notes in Mathematics, Vol. 962, 1982.
• (with J.-M. Cordier) Functors between shape categories, Jour. Pure Applied Alg., 27 (1983) pp. 1-13.
• The derived functors of Lim and protorsion modules, Cahiers Top. Géom. Diff., 24, (1983) pp. 115-131.
• Kernels of completion maps and a relative form of Nakayama's Lemma, Jour. Alg. 85 (1983) pp. 166-178.
• Categorical Shape Theory, Convegno di Topologia, Supplement to Rendi. Circ. Mat. Palermo II, 4 (1984) pp. 83-99.
• Homotopy Groups for Strong Shape and Proper Homotopy, Convegno di Topologie, Supplement to Rendi. Circ. Mat. Palermo II 4 (1984) pp. 101-113.
• Cohn's rings of zero divisors, Arch. Math. 43 (1984) pp. 340-343.
• A relative Jacobson radical with applications, in Radical Theory, Eger 1982, Colloquia Math. Soc. János Bolyai No. 38, North Holland, Amsterdam, pp. 405-448.
• Crossed Modules in Cat and a Brown-Spencer Theorem for 2-Categories, Cahiers Top. Géom. Diff., 26 (1985) pp. 381-387.
• (with G.J. Ellis) Free and Projective Crossed Modules and the Second Homology Group of a Group, Jour. Pure Applied Alg., 40 (1986) pp. 27-32.
• Homology of commutative algebras and an invariant of Simis and Vasconcelos, Jour. Alg., 99 (1986) pp. 458-465.
• (with J.-M. Cordier), Vogt's Theorem on Categories of Homotopy Coherent Diagrams, Math. Proc. Camb. Phil. Soc. 100 (1986) pp. 65-90.
• Some Categorical Results in the Theory of Crossed Modules in Commutative Algebras, Jour. Alg. 109 (1987) 415-429.
• Extensions, crossed modules and internal categories in categories of groups with operations, Proc. Edin. Math. Soc. 30 (1987) 373-381.
• (with J.-M. Cordier), Maps between homotopy coherent diagrams, Top. and its Applications, 28 (1988) 255-275.
• On the two definitions of Ho(proC), Top. and its Applications, 28 (1988) 289-293.
• (with L.J. Hernández), Proper pointed maps from R to a $\sigma$-compact space, Math. Proc. Camb. Phil. Soc. 103 (1988)457-462.
• (with L.J. Hernández), Global analogues of the Brown-Grossman proper homotopy groups of an end, Math. Proc. Camb. Phil. Soc. 104 (1988) 483-496.
• Crossed modules, crossed n-cubes and simplicial groups. Bull. Soc. Math. Belg. 41 (1989) 393-415.
• (with F.J. Korkes), Pro-C completions of crossed modules, Proc. Edin. Math. Soc. 33 (1990) 39-51.
• (with J.-M. Cordier), Fibrant diagrams, rectifications and a constuction of Loday, J.Pure Appl. Algebra, 67 (1990) 111-124.
• (with K.H.Kamps), Note on bridging theorems for semisimplicial sets, Quaestiones Mathematicae 13 (1990) 349-360.
• (with F.J.Korkes) Nilpotent crossed modules and pro-C completions, Cahiers Top. Géom. Diff.31 (1990) 277-282.
• 62. (with K.Hardie and K.H.Kamps), The coherent homotopy category over a fixed space is a category of fractions, Top. and its Appls. 40 (1991) 265-274.
• (with L.J.Hernández) Categorical Models of N-types for pro-crossed complexes and In-prospaces, in 1990 Barcelona Conference on Algebraic Topology, Springer Lecture Notes in Mathematics, No.1509, 1992.
• (with L.J.Hernández) An embedding theorem for proper n-types, Top. and its Applications, 48, (1992) 215-233 .
• n-Types of Simplicial Groups and Crossed n-cubes, Topology, 32, (1993) 5-24.
• (with Jean-Marc Cordier) Categorical Aspects of Equivariant Homotopy, Proc. ECCT, Applied Cat.Structures.4 (1996) 195-212.
• Interpretations of Yetter's notion of G-coloring : simplicial fibre bundles and non-abelian cohomology, J. Knot Theory and its Ramifications 5 (1996) 687-720.
• 68. (with Z.Arvasi) Simplicial and Crossed Resolutions of Commutative Algebras. J.Alg.181 (1996) 426-448.
• (with Z.Arvasi) Higher order Peiffer elements in Simplicial Commutative Algebras, T.A.C. 3, (1997), 1-23.
• (with R.Brown) On the Schreier theory of non-abelian extensions: generalisations and computations, (Proc.Royal Irish Acad., 96A, (1996) 213-227.
• (with Jean-Marc Cordier) Homotopy Coherent Category Theory, Trans. Amer. Math. Soc. 349 (1997) 1-54.
• (with P.J. Ehlers) Varieties of simplicial groupoids, I, Crossed complexes, Jour. Pure Applied Algebra, 120 (1997) 221 - 233.Erratum: Jour. Pure Applied Algebra, 134 (1999) 221-233.
• (with R.Brown, M.Golasi\'{n}ski and A.Tonks) Spaces of maps into classifying Spaces for equivariant crossed complexes, Indagationes Mathematica, 8 (1997) 157-172.
• Topological Quantum Field Theories from Homotopy n-types, J. London Math. Soc. (2) 58 (1998) 723-732.
• (with Z.Arvasi) Freeness conditions for 2-crossed modules of commutative algebras, Applied Categorical Structures, 6 (1998) 455-471.
• (with A.Mutlu) Applications of Peiffer pairings in the Moore complex of a simplicial group,Theory and Applications of Categories, 4, No. 7, (1998) 148-173.
• (with A.Mutlu) Freeness conditions for 2-crossed modules and complexes,Theory and Applications of Categories, 4, No. 8, (1998) 174-194.
• (with K.H. Kamps) A homotopy 2-groupoid from a fibration, Homology, Homotopy and Applications 1 (1999) 79-93 .
• (with A.Mutlu) Free crossed resolutions from simplicial resolutions with given $CW$-basis, Cahiers Top. Géom. Diff. catégoriques, 50 (1999) 261-283.
• (with P.J. Ehlers) Joins for (augmented) simplicial sets, Jour. Pure Applied Algebra, 145 (2000) 37-44.
• (with A.Mutlu) Freeness conditions for crossed squares and squared complexes, K-Theory, 20, (2000) 345 - 368.
• (with A.Mutlu) Iterated Peiffer pairings in the Moore complex of a simplicial group, Applied Categorical Structures, 9 (2001) 111-130.
• (with R.Brown, M.Golasinski and A.Tonks) Spaces of maps into Classifying Spaces for equivariant crossed complexes, II: the general topological case, K-Theory, 23 (2001) 129-155.
• (with R.Brown, K.A. Hardie and K.H. Kamps) A homotopy double groupoid of a Hausdorff space, Theory and Applications of Categories, 10. No.2, (2002) 71-93.
• (with M.V.Lawson and J.Matthews) The homotopy theory of inverse semigroups, Int. Journal of Algebra and Computation, 12 , (2002) 755-- 790.
• (with K.H.Kamps) 2-Groupoid Enrichments in Homotopy Theory and Algebra, K-Theory, 25 (2002) 373-409.
• Abstract Homotopy Theory, the interaction of category theory and homotopy theory, (survey article, updated version of lecture notes below, Cubo, 5 (2003)115-165, 2003)
• (with R. Brown, and M. Bullejos), Crossed complexes, free crossed resolutions and graph products of groups, in Recent Advances in Group Theory and Low-Dimensional Topology , Research and Exposition in Mathematics vol 27, Helderman Verlag, 2003, pp. 11-26
• (with R. Brown, E. Moore and C.D. Wensley), Crossed complexes, and free crossed resolutions for amalgamated sums and HNN-extensions of groups, Georgian Math. J., Special issue for the 70th birthday of H. Inissaridze, 9 (2002) 623 - 644.89.
• 90. Abstract Homotopy Theory, the interaction of category theory and homotopy theory, (survey article, updated version of lecture notes), Cubo Matematica Educacional 5, (2003), 115 - 165.
• (with R. Brown, and K. H. Kamps) A van Kampen theorem for the homotopy double groupoid of a Hausdorff space, Theory and Applications of Categories, 14, 2005, No. 9, 200-220.
• (with G. Donadze, and N. Inassaridze) N-fold Cech derived functors and generalised Hopf type formulas, K-Theory 35 (2005) 341 - 373.
• (with A. Bak, R. Brown and G. Minian), Global Actions, Groupoid Atlases and Applications, Journal of Homotopy and Related Structures, 1(1), 2006, pp.101 - 167.
• Formal Homotopy Quantum Field Theories II: Simplicial Formal Maps, Cont. Math. (Streetfest volume)( to appear)(available at ArXiv: math.QA/0512034).
• (with J. Faria Martins) On Yetter's Invariant and an Extension of the Dijkgraaf-Witten Invariant to Categorical Groups, Theory and Applications of Categories,18, 2007, No. 4, pp 118-150; (available also at ArXiv: math.QA/0608484)
• (with P.J.Ehlers) Ordinal subdivision and special pasting in quasicategories, Advances in Math. (2007), doi:10.1016/j.aim.2007.05.023 (Preprint available as 05.03 on Bangor preprint server)
• (with V. Turaev) Formal Homotopy Quantum Field Theories, I: Formal Maps and Crossed C-algebras, Journal of Homotopy and Related Structures (to appear).

### Lecture Notes

• J.-M. Cordier and T. Porter: Une introduction à la théorie de la forme, Esquisses Mathématiques No. 30, 1978, 138 pages.
• Homotopy Limits and Homotopy Coherence. A report on joint work by Jean - Marc Cordier and Timothy Porter, Quaderno del gruppo di ricerca Algebra-Geometria-Topologia 9, Università di Perugia, 1987, 123 pages.
• Proper Homotopy, Prohomotopy and Coherence, (Lecture Notes) Publ. Semin. Mat. Garcia de Galdeano, Serie II Seccion 3 No 10, 1987, 65 pages.
• Abstract Homotopy Theory, the interaction of category theory and homotopy theory, Notes for lectures at Bressanone, 2-6 September, 1991, Dipartimento di Matematica, Universita di Genova, N.199, Marzo 1992.
• Algebraic Models for Proper Homotopy Types, Lectures at Logro&ntildeno, November 1991, 28 pages, in Proceedings of the Workshop on Proper Homotopy Theory, Universidad de la Rioja,1993.
• S-categories, S-groupoids, Segal categories and quasicategories, Notes for lectures at Hagen and La Laguna, September 2003. (ArXiv: math.AT/0401274). also (Preprint 04.02))

### Artificial Intelligence, Computer Science, etc

• (with J.-M. Cordier), Pattern Recognition and Categorical Shape Theory, Pattern Recognition Letters, 7 (1988) 73-76.
• Can categorical shape theory handle grey level images? in Shape in Picture'', Proc. NATO advanced research workshop, NATO ASI Series F, Vol 126, Springer-Verlag, Berlin Heidelberg, 1994.
• Categorical shape theory as a formal language for pattern recognition, Annals of Mathematics and Artificial Intelligence, 10, (1994) 25-54.
• (with R.Brown) Mathematical Structure: Knowledge, Representation and Interpretation', in Theoria et Historia Scientiarum, the International Journal of Interdisciplinary Studies, special issue on Knowledge: representations and interpretations', edited W. Meyer and R. Paton. 6 (2002) 39-54.
• (with R. Brown and R.Paton)`Categorical language and hierarchical models for cell systems,' to appear in Computing in Cells and Tissues - Perspectives and Tools of Thought' , Springer Series on Natural Computing.
• Geometric Aspects of Multiagent Systems, Electronic Notes in Theoretical Computer Science 81 (2003) URL: http://www1.elsevier.com/gej-ng/31/29/23/139/23/show/Products/notes/index.htt .
• 7. (with R.Brown) The intuitions of higher dimensional algebra for the study of structured space, Géométrie et Cognition, G. Longo (Editeur), Numéro spécial de la Revue de Synthèse, 5e série, t.124, 2003, 173-203, Editions rue d’Ulm/Fondation “Pour la science”, ENS.
• (with R.Brown) Category Theory and Higher Dimensional Algebra: Potential Descriptive Tools in Neuroscience, Proc. Inter. Conf. Theoretical Neurobiology, NBRC, Conf Proc. 1, Manesar, India, Dec. 2003. (arXiv: math.CT/0306223)
• Interpreted systems and Kripke models for multiagent systems from a categorical perspective, Theoretical Computer Science, 323 (2004) pp. 235-266.
• (with R.Brown) Category Theory, an abstract setting for analogy and comparison, In: What is Category Theory? Advanced Studies in Mathematics and Logic. Polimetrica Publisher, Italy, (ISBN 88-7699- 031-3), pp. 257-274.
• (with J.Gratus), A Spatial View of Information, Theoretical Computer Science 365 (2006) 206-215.
• Enriched categories and models for spaces of evolving states, Theoretical Computer Science (to appear). .

## Proceedings Articles (non refereed)

• (with J.Gratus) A geometry of information, I: Nerves, posets and differential forms (on Dagstuhl seminar 04351 website).
• (with J.Gratus) A geometry of information, II: Sorkin models, and biextensional collapses (on Dagstuhl seminar 04351 website).
• Enriched categories and models for spaces of dipaths, (proceedings article for Dagstuhl Sem. 06341)

## Educational Articles

• Undergraduate Projects in Group Theory: Commutativity Ratios, Irish Math Soc. Newsletter No. 14, September, 1985, 44-49.
• Undergraduate Projects in Group Theory: Automorphism Groups, Irish Math. Soc. Bulletin No. 16, March, 1986, 69-72
• Group presentations, topology and graphs, Irish Math. Soc. Bulletin No. 22 (1989) 13-20.
• (with R.Brown), Making a Mathematical exhibition, in The Popularisation of Mathematics, Ed. A.G.Howson and J.-P.Kahane, ICMI Study Series, Cambridge University Press, 1990, p.51-64.,
• (with R.Brown), Mathematics in Context, A New Course, For the Learning of Mathematics, 10 (1990) 10-15.
• Mathematics and Education Policy, report for a Round Table at the ECM'92, available from the L.M.S. ftp archive (summary in LMS Newsletter).
• (with J.Camus) Mathematics and Education Policy, in les Actes du Congrès Européen de Mathématiques, 1992.
• (with R.Brown), The Methodology of Mathematics, I.C.M.I. Bulletin, No. 37, December 1994, and Maths. Gazette 79 No 485 July 1995, pp.321-334.
• Innovations in Mathematics Courses, report on survey for LMS available from the LMS ftp archive.
• (with R.Brown) Why choose mathematics? in Mathematics for the future, 93/94, revised for 94/94 edition, I.M.A. in conjunction with Hobsons Pub., 1993 and 1994.
• (with R. Brown) Analogy, concepts and methodology in mathematics, Eureka 58, The Archimideans, Cambridge Univ. Math. Soc., Sept. 2006.

## Reviews of Books

Reviews of:

• "Algebraic Homotopy'' by H.J.Baues, in Bull. London Math. Soc. 22 (1990) 196-197.
• "Fundamentals of Pattern Recognition'' by M.Pavel, in Mathematical Gazette and also in Zentrallblatt f\"{u}r Math.
• "Pattern Recognition and Image Preprocessing" by Sing-Tze Bow, in Mathematical Gazette.
• "Mathematical Morphology in Image Processing", edited by E.R. Dougherty, in Mathematical Gazette.
• "Shape and shape theory" by D.G.Kendall, D.Barden, T.K.Carne and H.Le, Bull. London Math. Soc. 32 (2000) 757-578.
• "Strong Shape Theory", by S. Mardesic, Bull. London. Math. Soc. 33 (2001) 125-126.
• "Triangulated Categories'', by A. Neeman, Annals of Mathematics Studies, vol. 148, (2001), Princeton U.P., for Bull. London Math. Soc. 34 (2002) 252-254.
• "Galois Theories", by F. Borceux and G. Janelidze, Cambridge Studies in Advanced Mathematics, 72, (2001), Cambridge University Press, for Edinburgh Math. Soc.
• “Vector Analysis”, by Klaus Janich, Springer UTM, (2000) for Maths Gazette.
• "Homotopy Limit Functors on Model Categories and Homotopical Categories, by W.G.Dwyer, P.S. Hirschhorn, D.M. Kan and J.H. Smith., Math Surveys and Monographs Vol 113, AMS.(2004), for Zbl MAth.

## Preprints or in Preperation

### Articles

• (with P.J.Ehlers) A van Kampen type metatheorem (provisional title).
• (with A. Mutlu) Crossed squares and 2-crossed modules,(Preprint 02.03)
• Algebraic Models for Multiagent Systems
• (with J. Gratus) A geometry of information, III: Differential graded algebras for discrete situations: the MRZ calculus.
• (with J.P. May), Weak categories.
• Topological Data Analysis: the topology of point data clouds.
• The Moore complex of a simplicial module ... and beyond, Article in Encyclopaedia of Mathematics, Editor: M. Hazewinkel, Kluwer, 2004.

### Books

• Profinite algebraic homotopy.

### Lecture Notes

• (with A. Bak, R. Brown, and G.Minian) Global Actions, Groupoid Atlases and Related Topics, Working Notes on the ARC project, Bangor-Bielefeld, 1998-2000, 106 pages already.
• Categorical Perspectives on Multiagent Systems, 59 pages already typed.
• The Crossed Menagerie: an introduction to crossed gadgetry in algebra and topology. (Notes prepared for the XVI Encuentro Rioplatense de Álgebra y Geometría Algebraica, in Buenos Aires, 12-15 December 2006) (available on demand.)
• The Crossed Menagerie: an introduction to crossed gadgetry and cohomology in algebra and topology. (Notes prepared for the XVI Encuentro Rioplatense de Álgebra y Geometría Algebraica, in Buenos Aires, 12-15 December 2006 and for course MATH5312, Spring-Summer term 2007, University of Ottawa) extended version of previous notes, 275 pages already.