DT-invariants from non-archimedean integrals
HARVARD-MIT ALGEBRAIC GEOMETRY
Dimitri Wyss - EPFL
Let $M(\beta,\chi)$ be the moduli space of one-dimensional semi-stable sheaves on a del Pezzo surface $S$, supported on an ample curve class $\beta$ and with Euler-characteristic $\chi$. Working over a non-archimedean local field $F$, we define a natural measure on the $F$-points of $M(\beta,\chi)$. We prove that the integral of a certain gerbe on $M(\beta,\chi)$ with respect to this measure is independent of $\chi$ if $S$ is toric. A recent result of Maulik-Shen then implies that these integrals compute the Donaldson-Thomas invariants of $M(\beta,\chi)$. A similar result holds for suitably twisted Higgs bundles. This is joint work with Francesca Carocci and Giulio Orecchia.