Twisted Teichmüller Curves

by Christian Weiß

Overview

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.

Product Details

ISBN-13:	9783319040745
Publisher:	Springer International Publishing
Publication date:	02/23/2014
Series:	Lecture Notes in Mathematics , #2104
Edition description:	2014
Pages:	166
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

Table of Contents

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.

Editorial Reviews

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)

From the Publisher