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Cylinder counts and spin refinement of area Siegel–Veech constants

Year: 2025

Type: article

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 Chen–Möller–Zagier (2018) and Chen–Möller–Sauvaget–Zagier (2020), 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.

Source: Commentarii Mathematici Helvetici

DOI: 10.4171/cmh/590

Authors: Jan-Willem van Ittersum, Adrien Sauvaget

Institutions: University of Cologne, Max Planck Institute for Mathematics, Analyse, Géométrie et Modélisation

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Universiteit Utrecht

OpenAlex ID: W4408446604

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