© 2014

Twisted Teichmüller Curves

  • 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 Lecture Notes in Mathematics book series (LNM, volume 2104)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Christian Weiß
    Pages 1-10
  3. Christian Weiß
    Pages 11-37
  4. Christian Weiß
    Pages 39-51
  5. Christian Weiß
    Pages 53-59
  6. Christian Weiß
    Pages 61-84
  7. Christian Weiß
    Pages 85-119
  8. Christian Weiß
    Pages 121-125
  9. Christian Weiß
    Pages 127-133
  10. Christian Weiß
    Pages 135-144
  11. Back Matter
    Pages 145-168

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.


14G35,20H10,11R11,37D40 Fuchsian groups Hilbert modular surfaces Real quadratic number fields Teichmüller curves Veech groups

Authors and affiliations

  1. 1.Institut für Algebra und GeometrieGoethe Universität Frankfurt am MainFrankfurt am MainGermany

Bibliographic information

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“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)