TY  - BOOK
AU  - Weib,Christian
TI  - Twisted teichmuller curves
T2  - Lecture notes in mathematics
SN  - 9783319040745 (hard cover : alk. paper)
U1  - 516.352 23
PY  - 2014///
CY  - Switzerland
PB  - Springer
KW  - Teichmüller spaces.
KW  - Algebraic Curves
KW  - Hilbert modular surfaces
N1  - Includes bibliographical references and index; 1. Introduction --
2. Background --
3. Teichmüller curves --
4. Twisted Teichmüller curves --
5. Stabilizer and maximality --
6. Calculations for twisted Teichmüller curves --
7. Prym varieties and Teichmüller curves --
8. Lyapunov exponents --
9. Kobayashi curves revisited--
A Appendix--
B Tables--
References--
Index
N2  - 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
ER  -