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Euler characteristics of Gothic Teichmüller curves

Martin Möller and David Torres-Teigell

Geometry & Topology 24 (2020) 1149–1210

We compute the Euler characteristics of the recently discovered series of Gothic Teichmüller curves. The main tool is the construction of “Gothic” Hilbert modular forms vanishing at the images of these Teichmüller 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.

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Teichmüller curves, Hilbert modular surfaces, theta functions, Lyapunov exponents
Mathematical Subject Classification 2010
Primary: 32G15
Secondary: 11F27, 11F46, 37D40
Received: 23 August 2018
Accepted: 2 June 2019
Published: 30 September 2020
Proposed: Benson Farb
Seconded: Anna Wienhard, Dan Abramovich
Martin Möller
Institut für Mathematik
Goethe–Universität Frankfurt
Frankfurt am Main
David Torres-Teigell
Institut für Mathematik
Goethe–Universität Frankfurt
Frankfurt am Main