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Twisted Teichmüller Curves

  • Book
  • © 2014

Overview

Authors:
  1. Christian Weiß

    1. Institut für Algebra und Geometrie, Goethe Universität Frankfurt am Main, Frankfurt am Main, Germany

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  • Contains a comprehensive introduction to the theory of Teichmüller curves
  • Is kept as self-contained as possible
  • Contains 15 figures and 2 tables

Part of the book series: Lecture Notes in Mathematics (LNM, volume 2104)

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Table of contents (9 chapters)

  1. Front Matter

    Pages i-xvi
    Download chapter PDF

  2. Introduction

    • Christian Weiß
    Pages 1-10

  3. Background

    • Christian Weiß
    Pages 11-37

  4. Teichmüller Curves

    • Christian Weiß
    Pages 39-51

  5. Twisted Teichmüller Curves

    • Christian Weiß
    Pages 53-59

  6. Stabilizer and Maximality

    • Christian Weiß
    Pages 61-84

  7. Calculations for Twisted Teichmüller Curves

    • Christian Weiß
    Pages 85-119

  8. Prym Varieties and Teichmüller Curves

    • Christian Weiß
    Pages 121-125

  9. Lyapunov Exponents

    • Christian Weiß
    Pages 127-133

  10. Kobayashi Curves Revisited

    • Christian Weiß
    Pages 135-144

  11. Back Matter

    Pages 145-168
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Keywords

About this book

These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmüller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objects are analyzed in detail and their main properties are described. In particular, the volume of twisted Teichmüller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples.

Reviews

“These notes contain detailed background material and a comprehensive survey of recent advances in the field. They can be used as a handbook for mathematicians who are interested in Teichmüller curves and Hilbert modular surfaces.” (Dawei Chen, Mathematical Reviews, February, 2016)

Authors and Affiliations

  • Institut für Algebra und Geometrie, Goethe Universität Frankfurt am Main, Frankfurt am Main, Germany

    Christian Weiß

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