Twisted Teichmüller Curves

• Main Author: Weiß, Christian (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Lecture Notes in Mathematics, 2104
• Subjects: Mathematics.; Algebraic geometry.; Dynamics.; Ergodic theory.; Number theory.; Algebraic Geometry.; Number Theory.; Dynamical Systems and Ergodic Theory.

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 part...

Table of Contents:

• Introduction
• Background
• Teichmüller Curves
• Twisted Teichmüller Curves
• Stabilizer and Maximality
• Calculations for Twisted Teichmüller Curves
• Prym Varieties and Teichmüller Curves
• Lyapunov Exponents
• Kobayashi Curves Revisited
• Appendix
• Tables
• List of Symbols
• Index
• Bibliography.