Extensions of period maps to toroidal compactifications

Date
2014/11/07 Fri 10:30 - 12:00
Room
3号館152号室
Speaker
Radu Laza
Affiliation
Stony Brook university / IAS
Abstract

It is a classical result of Mumford and Namikawa that the Torelli map extends to a morphism from the moduli of stable curves to the second Voronoi compactification of A_g. Recently, Alexeev and Brunyate showed that the Torelli map also extends to the perfect cone compactification, but fails to extend to the central cone. For Prym varieties, it is known by work of Friedman and Smith that the period fails to extend to the boundary for any of the standard toroidal compactifications of A_g. In this talk, I will discuss refinements of these extension results (e.g. indeterminacy loci, resolutions in low genus, etc.) for Prym varieties. These results are partially motivated by the study of the moduli space of cubic threefolds.