The Donaldson-Thomas theory of K3xE and the Igusa cusp form
-- Jim Bryan, November 21, 2014

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Donaldson-Thomas invariants are fundamental
deformation invariants of Calabi-Yau threefolds. We describe a
recent conjecture of Oberdieck and Pandharipande, which predicts
that the (three variable) generating function for the
Donaldson-Thomas invariants of K3 x E is given by the reciprocal
of the Igusa cusp form of weight 10. For each fixed K3 surface
of genus g, the conjecture predicts that the corresponding (two
variable) generating function is given by a particular
meromorphic Jacobi form. We prove the conjecture for K3
surfaces of genus 0 and genus 1. Our computation uses a new
technique which mixes motivic and toric methods.