On the asymptotics of determinant of Laplacian at the principal boundary of the principal stratum of the moduli space of Abelian differentials

TL;DR

This paper investigates the asymptotic behavior of the Laplacian determinant on translation surfaces as two conical points merge, revealing insights into the geometric and spectral properties near the boundary of the moduli space.

Contribution

It provides a detailed analysis of the Laplacian determinant asymptotics on translation surfaces during conical point collisions, advancing understanding of spectral geometry in moduli space boundaries.

Findings

Asymptotic formulas for Laplacian determinant near conical point collisions

Insights into the geometric structure of the moduli space boundary

Connections between spectral invariants and geometric degenerations

Abstract

We study the asymptotics of the determinant of Laplacian on a translation surface (a compact Riemann surface equipped with a conformal flat conical metric with trivial holonomy) of genus g with 2g-2 conical points of angle 4\pi as two conical points collide.