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Le problème de Schottky et la conjecture de Novikov. (The Schottky problem and the Novikov conjecture). (French) Zbl 0637.14021

Sémin. Bourbaki, 39ème année, Vol. 1986/87, Exp. 675, Astérisque 152/153, 101-112 (1987).
[For the entire collection see Zbl 0627.00006.]
The paper discusses a connection between the classical problem of finding a generic description for the variety of period matrices of compact Riemann surfaces with a given genus (Schottky problem) and the properties of generalized Kadomtsev-Petviashvili (K-P) equation over abelian varieties.
The connection stems firstly from the fact that the characterization of period matrices among all Siegel matrices is equivalent to characterization of Jacobians among the principally polarized abelian varieties (p.p.a.v.’s), and, secondly, from Novikov’s conjecture [proved by T. Shiota, Invent. Math. 83, 333-382 (1986; Zbl 0621.35097)] that a p.p.a.v., whose theta-function satisfies a K-P equation, is Jacobian.
Reviewer: A.Bocharev

MSC:

14K10 Algebraic moduli of abelian varieties, classification
14H40 Jacobians, Prym varieties
32G20 Period matrices, variation of Hodge structure; degenerations
14K25 Theta functions and abelian varieties
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