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Twisted Teichmüller Curves / by Christian Weiß.
Math/Physics/Astronomy Library QA3 .L28 v.1-999 470,523,830,849:2nd ed. v.1000-1722,1762,1781,1799-2099,2100-2192-2218 2219-2223-2258,2260-2271,2273-2274-2277,2279-2281,2283-2289,2291,2293-2294,2296,2298-2299,2300-2311,2313-2379,2381-2383 2385,2388-2389
Mixed Availability
LIBRA QA3 .L28 Scattered vols.
Mixed Availability
- Format:
- Book
- Author/Creator:
- Weiss, Christian, Author.
- Series:
- Lecture Notes in Mathematics, 0075-8434 ; 2104
- Language:
- English
- Subjects (All):
- Geometry, Algebraic.
- Number theory.
- Dynamics.
- Ergodic theory.
- Algebraic Geometry.
- Number Theory.
- Dynamical Systems and Ergodic Theory.
- Local Subjects:
- Algebraic Geometry.
- Number Theory.
- Dynamical Systems and Ergodic Theory.
- Physical Description:
- 1 online resource (XVI, 166 p. 13 illus., 6 illus. in color.)
- Edition:
- 1st ed. 2014.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2014.
- Language Note:
- English
- Summary:
- 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.
- 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.
- Notes:
- Expanded version of the author's thesis (doctoral)--Universität Frankfurt am Main.
- Includes bibliographical references (pages 159-163) and index.
- ISBN:
- 3-319-04075-8
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