Twisted Teichmüller Curves
Seiten
2014
|
2014
Springer International Publishing (Verlag)
978-3-319-04074-5 (ISBN)
Springer International Publishing (Verlag)
978-3-319-04074-5 (ISBN)
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.
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.
"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)
| Erscheint lt. Verlag | 7.3.2014 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics |
| Zusatzinfo | XVI, 166 p. 13 illus., 6 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 290 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| Schlagworte | 14G35,20H10,11R11,37D40 • Fuchsian Groups • Hilberf modular surfaces • Hilbert modular surfaces • Real quadratic number fields • Real quadratic number fiels • Teichmüller curves • Veech groups |
| ISBN-10 | 3-319-04074-X / 331904074X |
| ISBN-13 | 978-3-319-04074-5 / 9783319040745 |
| Zustand | Neuware |
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