Intersection theory and Siegel-Veech constants for Prym eigenform loci in $\Omega\mathcal{M}_3(2,2)^{\rm odd}$

TL;DR

This paper calculates Siegel-Veech constants for Prym eigenforms in a specific moduli space, enhancing understanding of geometric structures and counting problems in translation surfaces.

Contribution

It provides explicit computations of Siegel-Veech constants for Prym eigenforms in genus three, focusing on non-square discriminant cases in the odd component.

Findings

Explicit Siegel-Veech constants for Prym eigenforms in genus three.

New insights into saddle connection configurations on Prym eigenforms.

Advances in understanding geometric and dynamical properties of these surfaces.

Abstract

We compute the Siegel-Veech constants associated to saddle connections with distinct endpoints on Prym eigenforms for real quadratic orders with non-square discriminant in $\Omega \mathcal{M}_3(2,2)^{\rm odd}$.