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.

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