Beauville, Arnaud 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 Cited in 3 ReviewsCited in 3 Documents 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 Keywords:Kadomtsev-Petviashvili equation; period matrices of compact Riemann surfaces; Schottky problem; (K-P) equation; Jacobians; Novikov’s conjecture Citations:Zbl 0627.00006; Zbl 0621.35097 PDFBibTeX XML Full Text: Numdam EuDML