标题： 特征类和阿贝尔簇上 perverse sheaves 的 Hilbert-Poincaré 系列 显示英文标题

标题： Characteristic classes and Hilbert-Poincaré series for perverse sheaves on abelian varieties

摘要： 一个阿贝尔簇上的 perverse sheaf 的卷积幂定义了一类有趣的分枝局部系统，其几何结构仍然了解甚少。 我们证明了它们的通用秩的生成级数是一个形状非常简单的有理函数，对于对称卷积幂也存在类似的结果。 我们还给出了其他 Schur 函子在对偶阿贝尔簇上的特征类表示公式，作为例子，我们讨论了 Prym-Tjurin 变体的情况。 显示英文摘要

摘要： The convolution powers of a perverse sheaf on an abelian variety define an interesting family of branched local systems whose geometry is still poorly understood. We show that the generating series for their generic rank is a rational function of a very simple shape and that a similar result holds for the symmetric convolution powers. We also give formulae for other Schur functors in terms of characteristic classes on the dual abelian variety, and as an example we discuss the case of Prym-Tjurin varieties.