Prym varieties and the Schottky problem
Prym varieties and the Schottky problem
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Prym 品种和肖特基问题
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
A. Beauville
中科院分区：
文献类型：
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作者：
A. Beauville
G是主极化阿贝尔簇的模空间，jgc~q/g是雅可比轨迹。问题是在S/g中找到JG(或者更确切地说是它的闭包JG)的显式方程.在他们漂亮的论文[A-M]中，Andreotti和Mayer证明了JG是具有Dim Sing O>；g 4的主极化阿贝尔变种(A，O)的轨迹N~4的一个不可约分量.然后，他们给出了写出N~4的“显式”方程的过程。JG不可能等于N_4：在亏格4中，至少还有另外一个分量，即主极化阿贝尔簇的因子0，Un，其中有一个消零(即，使得Sing O包含一个2阶点)。我们的目标是证明以下几点：
be the moduli space of principally polarized abelian varieties of dimension g, Jg c ~q/g the locus of Jacobians. The problem is to find explicit equations for Jg (or rather its closure Jg) in s/g. In their beautiful paper [A-M], Andreotti and Mayer prove that Jg is an irreducible component of the locus N~_ 4 of principally polarized abelian varieties (A, O) with dim Sing O > g 4 . Then they give a procedure to write "explicit" equations for N~_ 4. There is no hope that Jg be equal to Ng_ 4: already in genus 4, there is at least one other component, namely the divisor 0,un of principally polarized abelian varieties with one vanishing theta-null (i.e. such that Sing O contains a point of order 2). Our aim is to prove the following: