Department of Mathematics, Aula Seminari.
We consider moduli spaces of one-dimensional semistable sheaves on del Pezzo and K3 surfaces supported on ample curve classes. Working over a non-archimedean local field $F$, we define a natural measure on the $F$-points of such moduli spaces. We prove that the integral of a certain naturally defined gerbe on the moduli spaces with respect to this measure is independent of the Euler characteristic. Analogous statements hold for (meromorphic or not) Higgs bundles. Recent results of Maulik-Shen and Kinjo-Coseki imply that these integrals compute the BPS invariants for the del Pezzo case and for Higgs bundles.
This is a joint work with Giulio Orecchia and Dimitri Wyss.
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