On invariants of moduli spaces of sheaves on Enriques surfaces - Special session of the HyperK seminar in Bonn on January 9 & 10, 2025

by Georg Oberdieck (Heidelberg)

Thursday Jan 9, 2025, 5:00 PM → 6:00 PM Europe/Berlin

Poppelsdorfer Allee 45, 1, EG, Lecture room - HIM PA82 (HIM)

Abstract: Under a suitable primitive assumption, moduli spaces of stable sheaves on Enriques surfaces are smooth projective varieties with torsion canonical bundle, which were proven by Beckmann and Nuer-Yoshioka to be birational to Hilbert schemes of points on the Enriques or compactified Jacobians (depending on whether the dimension is even or odd). While in 
the even-dimensional case this determines their Betti numbers, not much is known in the odd-dimensional case (b_1,b_2 was computed by Sacca). In this talk I will give an overview about recent curve counting results on 
the local Enriques surfaces and explain what they predict for the moduli spaces of sheaves. In particular, we will state a conjectural relation how the perverse Hodge numbers of the compactified Jacobians are determined by their Betti numbers, and give an asymptotic formula for their Betti numbers.