Twisted Teichmüller Curves [electronic resource] /Material type: BookSeries: Lecture Notes in Mathematics: 2104Publisher: Cham : Springer International Publishing : 2014.Description: XVI, 166 p. 13 illus., 6 illus. in color. online resource.ISBN: 9783319040752.Subject(s): Mathematics | Geometry, algebraic | Differentiable dynamical systems | Number theory | Mathematics | Algebraic Geometry | Number Theory | Dynamical Systems and Ergodic TheoryDDC classification: 516.35 Online resources: Click here to access online
|Item type||Current location||Call number||Status||Date due||Barcode|
Central Library, IISER Bhopal
OPAC URL: http://webopac.iiserb.ac.in/
|516.35 (Browse shelf)||Not for loan|
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 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.