Christina Birkenhake's Complex Abelian Varieties PDF

By Christina Birkenhake

ISBN-10: 3662027887

ISBN-13: 9783662027882

ISBN-10: 3662027909

ISBN-13: 9783662027905

This publication explores the idea of abelian forms over the sphere of complicated numbers, explaining either vintage and up to date ends up in sleek language. the second one version provides 5 chapters on fresh effects together with automorphisms and vector bundles on abelian forms, algebraic cycles and the Hodge conjecture. ". . . way more readable than such a lot . . . it's also even more complete." Olivier Debarre in Mathematical experiences, 1994.

Show description

Read Online or Download Complex Abelian Varieties PDF

Similar algebraic geometry books

Martin Schlichenmaier's An Introduction to Riemann Surfaces, Algebraic Curves and PDF

This ebook provides an advent to trendy geometry. ranging from an effortless point the writer develops deep geometrical techniques, taking part in a major position these days in modern theoretical physics. He offers a variety of concepts and viewpoints, thereby exhibiting the kinfolk among the choice techniques.

Read e-book online Topics in algebraic geometry and geometric modeling: PDF

Surveys, tutorials, and learn papers from a summer season 2002 workshop research various issues in algebraic geometry and geometric modeling. Papers are divided into sections on modeling curves and surfaces, multisided patches, implicitization and parametrization, subject types, and combined quantity and resultants, and papers from either disciplines are incorporated in every one part.

Get Brauer groups, Tamagawa measures, and rational points on PDF

The significant subject of this booklet is the learn of rational issues on algebraic different types of Fano and intermediate type--both by way of while such issues exist and, in the event that they do, their quantitative density. The ebook comprises 3 elements. within the first half, the writer discusses the idea that of a top and formulates Manin's conjecture at the asymptotics of rational issues on Fano forms.

Extra resources for Complex Abelian Varieties

Sample text

This proves the assertion. 2 we associated to every holomorphic line bundle on X an alternating Z-valued form on A and thus via JR-linear extension an alternating form V x V --t JR. Conversely, we will determine, which alternating forms come from line bundles in this way. 6) Proposition. For an alternating form E: V x V --t JR the following conditions are equivalent: i) There is a holomorphic line bundle L on X such that E represents the first Chern class c1 (L ) . ii) E(A, A) ~ Z and E(iv,iw) = E(v,w) for all v,w E V.

For all u = u l + u2,v = VI + v2, W E V = VI EB V2 a) adu,v + w) = aL(u,v)e(1fH(w,u)), b) aL(u + v, w) = aL(u, v + w)aL(v, w)e(21fiE(u l , V2))' c) adu,v)-I = aL(-u,v)Xo(u)-2 e(-1fH(u,u)), d) aL'(u,v) = aL(u,v)e(21fiE(w,u)) with L' = t':nL. Proof. 2 respectively. 1: aL(u+v,W) = = Xo(u + v)e(21fiE(c, u + v) = + 1fH(w, u + v) + ~H(u + v, u + v)) Xo(u)e(21fiE(c,u) + 1fH(v + w,u) + ~H(u,u)) . Xo(v)e(21fiE(c, v) + 1fH(w, v) + ~H(v, v)) . e(1fiE(u,v) - 21fiE(U2' VI) = + ~H(u,v) - aL(u,v+w)adv,w)e(21fiE(UI,V2)) .

Then c1(/* M) = H, and thus L ® /* M- 1 E Pic°(X1). 3 the homomorphism /*: Pic°(X2) ---- Pic°(X1) is surjective, so there is an N E Pic°(X2) with /* N = L ® /* M- 1. Now M = M ® N satisfies i). 4. D Let L be a line bundle on X. For any point x E X the line bundle t;L®L- 1 has first Chern class zero. 3 is a homomorphism. In order to compute its analytic representation, suppose L = L(H, X) and X = VIA. 5) Lemma. The map

Download PDF sample

Complex Abelian Varieties by Christina Birkenhake

by Richard

Rated 4.43 of 5 – based on 12 votes