English

Cylinder counts and spin refinement of area Siegel-Veech constants

Algebraic Geometry 2022-11-01 v1 Differential Geometry Representation Theory

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.

Keywords

Cite

@article{arxiv.2210.17374,
  title  = {Cylinder counts and spin refinement of area Siegel-Veech constants},
  author = {Jan-Willem van Ittersum and Adrien Sauvaget},
  journal= {arXiv preprint arXiv:2210.17374},
  year   = {2022}
}

Comments

42 pages, 4 figures