Seminari del Dipartimento di Matematica

Seminario del 2024

Georg Oberdieck

Curve counting on the Enriques surface and Borcherds automorphic form

nell'ambito della serie: SEMINARIO DI ALGEBRA E GEOMETRIA

algebra e geometria

An Enriques surface is the quotient of a K3 surface by a fixed point-free involution. Klemm and Marino conjectured a formula expressing the Gromov–Witten invariants of the local Enriques surface in terms of automorphic forms. In particular, the generating series of elliptic curve counts on the Enriques should be the Fourier expansion of (a certain power of) Borcherds famous automorphic form on the moduli space of Enriques surfaces. In this talk I will explain a proof of this conjecture.