Download Algebraic Surfaces by Lucian Badescu, V. Masek PDF

By Lucian Badescu, V. Masek

This publication provides basics from the idea of algebraic surfaces, together with components reminiscent of rational singularities of surfaces and their relation with Grothendieck duality idea, numerical standards for contractibility of curves on an algebraic floor, and the matter of minimum versions of surfaces. in reality, the category of surfaces is the most scope of this publication and the writer provides the method built through Mumford and Bombieri. Chapters additionally hide the Zariski decomposition of powerful divisors and graded algebras.

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2). 1. 4, et sous l'hypoth~se suppldmentaire, sans doute superf6tatoire (conjecture de Bloch sur les surfaces avec H 2(X, Ox) = 0), que l'application d'A1banese A0(X) ~ Al_~bx(k) est un isomorphisme, Saito [$2] d6montre qu'en fait t'accouplement Ao(X) x B r ( X ) ~ Q/Z est non d6g6n6r6 £ gauche. __qc~),Q / l ) . gc°),Q/Z). l Hom(Br(X),Q/i[) l-" Ainsi le noyau de la fl~che verticale de gauche est inclus dans le noyau de la fl~che horizontale sup6rieure, qui par l'hypoth~se suppl@mentaire est un groupe de torsion.

P. ) Kluwer Academic Publishers 1989. [R3] W. - - On g l of curves over global fields, Math. Ann. 288 (1990) 179-193. IS1] S. SAITO. F. P. ) Kluwer Academic Publishers 1989. [$2] S. - - A conjecture of Bloch and Brauer groups of surfaces over p-adic fields, preprint, May 1990. [$3] S. SAITO. --- Torsion zero-cycles and 6taie homology of singular schemes, Duke Math. J. 64 (1991) 71-83. [$4] S. SAITO. - - Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991) 443-460. [Sbl] P.

4] S. SAITO. - - Cycle map on torsion algebraic cycles of codimension two, Invent. Math. 106 (1991) 443-460. [Sbl] P. - - Zero-cycles on rational surfaces over number fields, Invent. Math. 91 (1988) 505-524. [Sb2] P. SALBERGER. - - Chow groups of codimension two and l-adic realizations of motivic cohomology, typescript, September 1991. [Sc] C. SoloEd. - - Some examples of torsion in the Griffiths group, Math. Ann. 293 (1992) 651-679. [ S o ] M. - On Milnor K-groups attached to semi-abelian varieties, Journal of K-theory 4 (1990) 105-119.

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