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Contains a comprehensive introduction to the theory of Teichmüller curves
Is kept as self-contained as possible
Contains 15 figures and 2 tables
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.
Content Level »Research
Keywords »14G35,20H10,11R11,37D40 - Fuchsian groups - Hilbert modular surfaces - Real quadratic number fields - Teichmüller curves - Veech groups