Twisted Teichmüller Curves

Nonfiction, Science & Nature, Mathematics, Number Theory, Geometry
Cover of the book Twisted Teichmüller Curves by Christian Weiß, Springer International Publishing
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Author: Christian Weiß ISBN: 9783319040752
Publisher: Springer International Publishing Publication: February 21, 2014
Imprint: Springer Language: English
Author: Christian Weiß
ISBN: 9783319040752
Publisher: Springer International Publishing
Publication: February 21, 2014
Imprint: Springer
Language: English

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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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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