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Twisted Teichmüller Curves de Christian Weiß

Twisted Teichmüller Curves: Lecture Notes in Mathematics, cartea 2104

Autor Christian Weiß
en Limba Engleză Paperback – 7 mar 2014
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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Specificații

ISBN-13: 9783319040745
ISBN-10: 331904074X
Pagini: 184
Ilustrații: XVI, 166 p. 13 illus., 6 illus. in color.
Dimensiuni: 155 x 235 x 10 mm
Greutate: 0.27 kg
Ediția:2014
Editura: Springer International Publishing
Colecția Springer
Seria Lecture Notes in Mathematics

Locul publicării:Cham, Switzerland

Public țintă

Research

Cuprins

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.

Recenzii

“These notes contain detailed background material and a comprehensive survey of recent advances in the field. They can be used as a handbook for mathematicians who are interested in Teichmüller curves and Hilbert modular surfaces.” (Dawei Chen, Mathematical Reviews, February, 2016)

Textul de pe ultima copertă

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.

Caracteristici

Contains a comprehensive introduction to the theory of Teichmüller curves Is kept as self-contained as possible Contains 15 figures and 2 tables