Twisted Teichmüller Curves
Weiß, Christian.
Twisted Teichmüller Curves [electronic resource] / by Christian Weiß. - XVI, 166 p. 13 illus., 6 illus. in color. online resource. - Lecture Notes in Mathematics, 2104 0075-8434 ; . - Lecture Notes in Mathematics, 2104 .
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.
9783319040752
10.1007/978-3-319-04075-2 doi
Geometry, algebraic.
Number theory.
Differentiable dynamical systems.
Algebraic Geometry.
Number Theory.
Dynamical Systems and Ergodic Theory.
QA564-609
516.35
Twisted Teichmüller Curves [electronic resource] / by Christian Weiß. - XVI, 166 p. 13 illus., 6 illus. in color. online resource. - Lecture Notes in Mathematics, 2104 0075-8434 ; . - Lecture Notes in Mathematics, 2104 .
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.
9783319040752
10.1007/978-3-319-04075-2 doi
Geometry, algebraic.
Number theory.
Differentiable dynamical systems.
Algebraic Geometry.
Number Theory.
Dynamical Systems and Ergodic Theory.
QA564-609
516.35