Collection Algèbre, Géométrie et Physique : une conférence en l'honneur
Organizer(s)
Date(s)
26/04/2024
The Katz-Klemm-Vafa formula
I will describe joint work with Rahul Pandharipande proving the Katz-Klemm-Vafa conjecture. This expresses the Gromov-Witten theory of K3 surfacesand K3-fibred 3-folds –in all genera and for all multiple covers –in terms of modular forms. We use Pandharipande-Pixton’s proof of the MNOP conjecture for many 3-folds and a new result on stable pairs and Noether-Lefschetz loci to translate the probleminto a computation of stable pair invariants. This is carried out using a degeneration formula and a vanishing result.
