Cylinder counts and spin refinement of area Siegel-Veech constants

2022/10/31 by Jan‐Willem van Ittersum, van Ittersum, Jan-Willem, Adrien Sauvaget +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Dynamics and Fractals #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2210.17374

openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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• Virtual volumes of strata of meromorphic differentials with simple poles

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