Euler characteristics of Gothic Teichm\"{u}ller curves
Algebraic Geometry
2020-10-07 v2 Geometric Topology
Abstract
We compute the Euler characteristics of the recently discovered series of Gothic Teichm\"{u}ller curves. The main tool is the construction of 'Gothic' Hilbert modular forms vanishing at the images of these Teichm\"{u}ller curves. Contrary to all previously known examples, the Euler characteristic is not proportional to the Euler characteristic of the ambient Hilbert modular surfaces. This results in interesting 'varying' phenomena for Lyapunov exponents.
Keywords
Cite
@article{arxiv.1807.10260,
title = {Euler characteristics of Gothic Teichm\"{u}ller curves},
author = {Martin Möller and David Torres-Teigell},
journal= {arXiv preprint arXiv:1807.10260},
year = {2020}
}
Comments
Revised version with minor corrections. Final version to appear in Geometry & Topology. 48 pages, 3 figures