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Quadric rank loci on moduli spaces of curves and K3 surfaces

Recent Progress in Moduli Theory May 06, 2019 - May 10, 2019

May 06, 2019 (03:30 PM PDT - 04:30 PM PDT)
Speaker(s): Gavril Farkas (Humboldt-Universität)
Location: MSRI: Simons Auditorium
  • Moduli space of curves

  • K3 surfaces

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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.

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