Emmy-Noether-Seminar

$\chi$-independence for K3 surfaces

Paul Ziegler (Regensburg)

Abstract: BPS invariants naturally appear in the enumerative geometry of sheaves with one-dimensional support on a Calabi-Yau threefold. Toda conjectured that these invariants are independent of the appearing Euler characteristic $\chi$. I will give an introduction to these concepts and talk about work in progress with M. Groechenig and D. Wyss proving this conjecture in the K3 case. We argue by relating BPS cohomology to p-adic integration on moduli stacks of sheaves, for which $\chi$-independence was shown by Carocci-Orecchia-Wyss. For this, we use a local description of these moduli stacks of sheaves in terms of moduli stacks of quiver representations.