Cylinder counts and spin refinement of area Siegel–Veech constants

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.