论文标题
高斯地图和肖特基问题的半持续性
Semicontinuity of Gauss maps and the Schottky problem
论文作者
论文摘要
我们表明，在家庭中，关于阿贝里亚品种的高斯图的程度是半连接的，我们研究了它的跳跃基因座。作为应用程序，我们可以获得在theta分裂的情况下，该学位回答了Schottky问题。我们的证明通过在cotangent束上专业化拉格朗日周期来计算高斯图的程度。我们还为与阿伯利亚品种有限的形态有有限的形态的交点共同体学获得了类似的结果。得出的是，包括肖特基基因座在内的Andreotti-Mayer基因座的许多组成部分都是由Theta Divisor的拓扑类型定义的PPAV模量空间的一部分。
We show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application we obtain that in the case of theta divisors this degree answers the Schottky problem. Our proof computes the degree of Gauss maps by specialization of Lagrangian cycles on the cotangent bundle. We also get similar results for the intersection cohomology of varieties with a finite morphism to an abelian variety; it follows that many components of Andreotti-Mayer loci, including the Schottky locus, are part of the stratification of the moduli space of ppav's defined by the topological type of the theta divisor.
