Algebraic Geometry Seminar
Gavril Farkas
Humboldt University of Berlin
Quadric rank loci on moduli of curves and K3 surfaces
Abstract: Given two vector bundles E and F on a variety X and a
morphism from Sym^2(E) to F, we compute the cohomology class of the
locus in X where the kernel of this morphism contains a quadric of
prescribed rank. Our formulas have many applications to moduli theory:
(i) a simple proof of Borcherds' result that the Hodge class on the
moduli space of polarized K3 surfaces of fixed genus is of
Noether-Lefschetz type, (ii) an explicit canonical divisor on the
Hurwitz space parametrizing degree k covers of the projective line
from curves of genus 2k-1, (iii) a closed formula for the Petri
divisor on the moduli space of curves consisting of canonical curves
which lie on a rank 3 quadric and (iv) myriads of effective divisors
of small slope on M_g. Joint work with Rimanyi.
Monday October 14, 2019 at 4:00 PM in 427 SEO