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The Schottky problem from the metric geometric perspective

The Schottky problem from the metric geometric perspective
Date:

30.05.2017

Place:

1.067 (20.30)

Speaker:

Lizhen Ji

Time:

17:00-18:00

Source:

The Schottky problem from the metric geometric perspective

The moduli space of compact Riemann surfaces of genus 1 can be identified with the quotient of the upper half plane by the modular group SL(2, Z). It admits two important generalizations: the moduli space M_g of compact Riemann surfaces of genus g greater than or equal to 1, and the moduli space A_g of principally polarized abelian varieties of dimension g. Besides various similarities between them, there is a period (or Jacobian) map from M_g to A_g. The classical Schottky problem is to understand the image of M_g in A_g. Besides being a quasi-projective variety, A_g is also a locally symmetric space of finite volume with respect to the invariant metric. We will discuss several results on the size, location and shape of the image of M_g with respect to this complete metric of A_g.