Masur-Veech volume of the gothic locus

Abstract

We calculate the Masur-Veech volume of the gothic locus $\mathcal{G}$ in the stratum $\mathcal{H}(2^3)$ of genus four. Our method is based on the use of the formulae for the Euler characteristics of gothic Teichmüller curves to determine the number of lattice points of given area. We also use this method to recalculate the Masur-Veech volumes of the Prym loci ${\mathcal{P}}_3\subset \mathcal{H}(4)$ and ${\mathcal{P}}_4\subset \mathcal{H}(6)$ in genus three and four.

arXiv commentRevised version with some corrections. Final version to appear in J. Lond. Math. Soc. 33 pages

References in corpus (8)

• Asymptotics of numbers of branched coverings of a torus and volumes of moduli spaces of holomorphic differentials
• Euler characteristics of Teichmüller curves in genus two
• Masur-Veech volumes and intersection theory on moduli spaces of abelian differentials
• Topological recursion for Masur-Veech volumes
• Weierstrass Prym eigenforms in genus four
• Enumeration of meanders and Masur-Veech volumes
• Complete periodicity of Prym eigenforms
• Euler characteristics of Gothic Teichmüller curves

Cited by in corpus (2)

• Variation of Hodge structure and enumerating tilings of surfaces by triangles and squares
• Dynamical invariants and intersection theory on the flex and gothic loci