The K. P. hypothesis for decomposable abelian varieties
type: Item
instance of: scholarly article
title: The K. P. hypothesis for decomposable abelian varieties
zbMATH Open document ID: 0912.14011
DOI: 10.1007/BF02677835
author: Giambattista Marini
published in: Manuscripta Mathematica
publication date: 1998-05-03T00:00:00Z
full work available at URL: https://eudml.org/doc/156320
review text: Novikov's conjecture states that the Kadomtsev-Petviashvili (K.P.) equation characterizes Jacobians among all the indecomposable principally polarized abelian varieties. Shiota gave a geometrical proof of this conjecture. The aim of this article is to include the decomposable case in Shiota's theorem: Theorem 2. Let \((X,\left[ \Theta \right])\) be a principally polarized abelian variety and let \(\Theta \) be a generator of the vector space \( H^0(X,{\mathcal O}(\Theta)).\) Assume that there exist invariant vector fields \( D_1\neq 0,D_2,D_3\) and a constant \(d\) such that the K.P. equation \( K.P.(D_1,D_2,D_3;d)=0\) holds. Then there exists a non-zero Jacobian \( (Y,\left[ \Theta _Y\right])\) and a p.p.a.v. \((Z,\left[ \Theta _Z\right])\) such that \((X,\left[ \Theta \right])\) is isomorphic to the product of the p.p.a.v. \((Y,\left[ \Theta \right])\times (Z,\left[ \Theta _Z\right])\) and the vector fields \(D_1\) and \(D_2\) are parallel to the tangent bundle \(T(Y).\)
Mathematics Subject Classification ID: 14H42
Mathematics Subject Classification ID: 14K25
Mathematics Subject Classification ID: 14H40
zbMATH DE Number: 1138670
zbMATH Keywords: Novikov's conjecture
zbMATH Keywords: Jacobians
zbMATH Keywords: Kadomtsev-Petviashvili equation
zbMATH Keywords: principally polarized abelian varieties
zbMATH Keywords: Jacobian
reviewed by: V. V. Chueshev
MaRDI profile type: Publication
cites work: Q3348102
cites work: Q4023939
cites work: Q4391357
cites work: Characterization of Jacobian varieties in terms of soliton equations
OpenAlex ID: W2082692186
description: scientific article; zbMATH DE number 1138670