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Twisted teichmuller curves / Christian Weib.

By: Material type: TextTextSeries: Lecture notes in mathematics ; 2104.Publication details: Switzerland : Springer, 2014.Description: xvi, 166 p. : illustrations ; 24 cmISBN:
  • 9783319040745 (hard cover : alk. paper)
Subject(s): DDC classification:
  • 516.352 23 W415
Contents:
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.
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.
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Holdings
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
Total holds: 0

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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