Irrationality of moduli spaces

Abstract: I will talk about the problem of determining the birational complexity of moduli spaces of curves and K3 surfaces. I will recall some recently introduced invariants that measure irrationality and talk about what is known for these moduli spaces. In the second half I will report on joint work with D. Agostini and K.-W. Lai, where we study how the degrees of irrationality of the moduli spaces of polarized K3 surfaces grow with respect to the genus g. We provide polynomial bounds. The proof relies on Kudla's modularity conjecture for Shimura varieties of orthogonal type. For special genera we exploit the deep Hodge theoretic relation between K3 surfaces and special hyperkähler fourfolds to obtain much sharper bounds.

mathematical physicsalgebraic geometrydifferential geometrygeometric topologyoperator algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry, Physics, and Representation Theory Seminar

Series comments: If you would like to receive announcements, please join our mailing list here: listserv.neu.edu/cgi-bin/wa?SUBED1=GPRT-SEMINAR&A=1