标题： theta除子的Gauss映射的次数 显示英文标题

标题： The degree of the Gauss map of the theta divisor

摘要： 我们研究了主极化复阿贝尔簇的theta除子的高斯映射的次数。 我们利用这一点来获得theta除子在其奇异点的不可约分支上的重数的界限，并在示例中应用这个界限，以理解孤立奇异点的局部结构。 我们进一步通过高斯映射的次数定义了ppavs模空间的分层。 在四维情况下，我们证明这种分层给出了施托克问题的一个弱解，并且我们猜想这在任何维度都成立。 显示英文摘要

摘要： We study the degree of the Gauss map of the theta divisor of principally polarised complex abelian varieties. We use this to obtain a bound on the multiplicity of the theta divisor along irreducible components of its singular locus, and apply this bound in examples, and to understand the local structure of isolated singular points. We further define a stratification of the moduli space of ppav's by the degree of the Gauss map. In dimension four, we show that this stratification gives a weak solution of the Schottky problem, and we conjecture that this is true in any dimension.