Spin volumes of minimal strata and Chiodo integrals

Abstract: We derive a closed formula for the Masur-Veech volumes of spin-parity components of the stratum of abelian differentials with a single zero of maximal order. Our approach is based on the intersection theory of the virtual subcone of spin-parity squares inside the Hodge bundle, recently developed by Holmes-Politopoulos-Sauvaget. This is a spin refinement of a classical result of Sauvaget and agrees with the lattice-point counting technique of Chen-Möller-Sauvaget-Zagier. We further apply this theory to compute spin counterparts of virtual volumes, defined recently by Sauvaget. These virtual volumes are related to area Siegel-Veech constants and we are able to compute these invariants component-wise. In addition, by comparing our method for non-parity squares with the classical result of Sauvaget, we compute specific Chiodo integrals.