On a Schottky problem for the singularlocus of A_5

摘要

Let Sing M_g be the singular locus of the moduli space of compact connected Riemann surfaces of genus g and SingA_g be the singular locus of the moduli space of principally polarized abelian varieties of dimension g. In this survey: we review the main analogies and differences among the results on automorphisms of Riemann surfaces and principally polarized abelian varieties, we describe and compare the sublocus of SingA_5 corresponding to Jacobians of Riemann surfaces with the sublocus corresponding to intermediate Jacobians of smooth cubic threefolds and we solve a Schottky problem for the 0-dimensional singular locus of A_5.