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Title:
Quadric rank loci on moduli spaces of curves and K3 surfaces

Speaker:
Gavril Farkas

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. This formula has many applications to moduli theory of which we mention: (i) a simple proof of Borcherds' and Pandharipande's 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) myriads of effective divisors of small slope on the moduli space of curves. This is joint work with Rimanyi.

Link:
https://www.msri.org/workshops/869/schedules/26613

Workshop:
MSRI- Recent Progress in Moduli Theory