By A.N. Parshin (editor), I.R. Shafarevich (editor), I. Rivin, V.S. Kulikov, P.F. Kurchanov, V.V. Shokurov

ISBN-10: 3540546812

ISBN-13: 9783540546818

This two-part EMS quantity presents a succinct precis of advanced algebraic geometry, coupled with a lucid advent to the hot paintings at the interactions among the classical sector of the geometry of advanced algebraic curves and their Jacobian kinds. a superb better half to the older classics at the topic.

**Read Online or Download Algebraic geometry 03 Complex algebraic varieties, Algebraic curves and their Jacobians PDF**

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**Additional resources for Algebraic geometry 03 Complex algebraic varieties, Algebraic curves and their Jacobians**

**Sample text**

V azK = -g <'r

13 the first Chern class of M vanishes. 2 Proposition: (i) All products c~ • •• ·c~ "1 "k vanish if I:A. >.!! K - 2 (ii) If M is in addition Kahler, then all Chern classes of M vanish. Proof: Computing the Chern forms first with respect to the holomorphic connection and then with respect to the connection associated to some hermitian metric, we see that [a] = c"-1 .... c"-k = [a] for any "1 ' .. '"-k' where a is a holomorphic (2·I:A. K,o)-form, and a is a real (I:A. K,I:A. K)-form. e • a = 0. a we infer Thus ( i) is proven.

3. 4 of the lift of ~ toM can involve only the Euclidean and the hermitian symmetric factors. 8 If M is Kahler-Einstein with non-zero (and hence definite) Ricci tensor, and if for some m > o there is a non-zero global section either in smne ® Km or in smnSG 1 ® K-m, then there is a hermitian symmetric factor in the de Rham ~ decomposition of M. 9 Suppose now~= s 2n(h) EH 0 (M,s 2nSG 1 ®K- 2 ), where his a conformal metric on M. Since h is nowhere degenerate, the decomposition of the lift of ~ to M must involve all factors 63 of the de Rharn decomposition.

### Algebraic geometry 03 Complex algebraic varieties, Algebraic curves and their Jacobians by A.N. Parshin (editor), I.R. Shafarevich (editor), I. Rivin, V.S. Kulikov, P.F. Kurchanov, V.V. Shokurov

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