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Cylinder counts and spin refinement of area Siegel-Veech constants

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arxiv 2210.17374 v1 pith:7D4AGTHP submitted 2022-10-31 math.AG math.DGmath.RT

Jan-Willem van Ittersum , Adrien Sauvaget This is my paper · ORCID
classification math.AGmath.DGmath.RT
keywords constantssiegel-veechareaarxivspinstrataabelianalong
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We study the area Siegel-Veech constants of components of strata of abelian differentials with even or odd spin parity. We prove that these constants may be computed using either: (I) quasimodular forms, or (II) intersection theory. These results refine the main theorems of arXiv:1606.04065 and arXiv:1901.01785 which described the area Siegel-Veech constants of the full strata. Along the proof of (II), we establish a new identity for Siegel-Veech constants of cylinders.

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  1. DR cycles and strata of differentials with spin parity

    math.AG 2025-09 conditional novelty 8.0 of 10

    The parity-refined classes of strata of k-differentials are tautological and explicitly computable, via a spin double ramification cycle formula and Segre classes of cones of spin sections.

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