arXiv subjects

Stijn Velstra

Publications and source records attributed to Stijn Velstra.

2 recordsLinked to original sources

arXiv2026

Spin volumes of minimal strata and Chiodo integrals

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-M\"oller-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.

math.AG↗

arXiv2025

Spin refinement of moduli spaces of residueless meromorphic differentials and the BKP hierarchy

We consider strata of curves carrying a residueless meromorphic differential inducing a spin structure on the curve. The cohomology classes of the closures of these strata, weighted by the parity of the spin structures, form a partial cohomological field theory (CohFT) of infinite rank. After applying the DR hierarchy construction to this partial CohFT and reducing to differentials with two zeros and arbitrarily many poles, we show that the resulting system of evolutionary PDEs coincides with the BKP hierarchy up to a coordinate transformation. This is a spin refinement of an analogous result from arXiv:2110.01419. Our proof relies on a new result regarding the reconstruction of the BKP hierarchy from a limited amount of information in the Lax formalism.

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