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.
Rezensionen / Stimmen
"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)
Reihe
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
7
6 farbige Abbildungen, 7 s/w Abbildungen
XVI, 166 p. 13 illus., 6 illus. in color.
Dateigröße
ISBN-13
978-3-319-04075-2 (9783319040752)
DOI
10.1007/978-3-319-04075-2
Schweitzer Klassifikation
