The Riemann-Schottky problem via singularities of theta divisors

  • Ruijie Yang (Max Planck Institute for Mathematics, Bonn)
E1 05 (Leibniz-Saal)


The Riemann-Schottky problem is the problem of determining which principally polarized abelian varieties (PPAV) arise as Jacobian of curves. Riemann showed that the theta divisor on the Jacobian of a hyperelliptic curve has singularity of codimension three. Beauville conjectured that any irreducible PPAV whose theta divisors have singularity of codimension three actually come from hyperelliptic curves. In this talk, I will discuss a refinement of this problem and a partial solution. To achieve this, we develop a theory of higher multiplier ideals for Q-divisors using the theory of complex Hodge modules of Sabbah-Schnell, building on M.Saito’s theory of rational Hodge modules. This is joint work with Christian Schnell.

Saskia Gutzschebauch

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Daniele Agostini

Max Planck Institute for Mathematics in the Sciences

Christian Lehn

Technische Universität Chemnitz

Rainer Sinn

Universität Leipzig