FRG workshop, 2011

B. Bakker

Title: Higher stable pair invariants for K3 surfaces


Virtual curve counts have been de%Gfi%@ned for threefolds by integration against virtual classes on moduli spaces of stable maps (Gromov-Witten theory), ideal sheaves (Donaldson-Thomas theory), and stable pairs (Pandharipande-Thomas theory); all three theories are conjecturally equivalent, and one might ask if the equivalence holds in other dimensions. The Gromov-Witten theory of K3 surfaces has recently been calculated by Maulik, Pandharipande, and Thomas, who further show that the partition functions are governed by classical modular forms. It is likewise equivalent to an analog of Pandharipande-Thomas theory for surfaces. In joint work with Andrei Jorza, we define and fully compute higher rank stable pair invariants on K3 surfaces in primitive classes. We show that the resulting invariants fully recover the Gromov-Witten theory, and that the partition functions are similarly comprised of modular forms.