Twisted teichmuller curves / Christian Weib.
Material type:
TextSeries: Lecture notes in mathematics ; 2104.Publication details: Switzerland : Springer, 2014.Description: xvi, 166 p. : illustrations ; 24 cmISBN: - 9783319040745 (hard cover : alk. paper)
- 516.352 23 W415
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 516.352 W415 (Browse shelf(Opens below)) | Available | 135840 |
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| 516.352 W146 A Theory of dormant opers on pointed stable curves/ | 516.352 W183 Algebraic curves | 516.352 W318 Elliptic curves : number theory and cryptography / | 516.352 W415 Twisted teichmuller curves / | 516.352 W474 Isosurfaces : | 516.352 Y94 The Gross-Zagier formula on Shimura curves / | 516.352 Z37 Algebraic surfaces |
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.
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.
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