Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2024 MCQ for Journal of the American Mathematical Society is 4.83.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Variations of Hodge structures of a Teichmüller curve
HTML articles powered by AMS MathViewer

by Martin Möller;
J. Amer. Math. Soc. 19 (2006), 327-344
DOI: https://doi.org/10.1090/S0894-0347-05-00512-6
Published electronically: December 12, 2005

Abstract:

Teichmüller curves are geodesic discs in Teichmüller space that project to an algebraic curve in the moduli space $M_g$. We show that for all $g \geq 2$ Teichmüller curves map to the locus of real multiplication in the moduli space of abelian varieties. Observe that McMullen has shown that precisely for $g=2$ the locus of real multiplication is stable under the $\textrm {SL}_2({\mathbb {R}})$-action on the tautological bundle $\Omega M_g$. We also show that Teichmüller curves are defined over number fields and we provide a completely algebraic description of Teichmüller curves in terms of Higgs bundles. As a consequence we show that the absolute Galois group acts on the set of Teichmüller curves.
References
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 32G15, 14D07
  • Retrieve articles in all journals with MSC (2000): 32G15, 14D07
Bibliographic Information
  • Martin Möller
  • Affiliation: Universität Essen, FB 6 (Mathematik), 45117 Essen, Germany
  • Email: martin.moeller@uni-essen.de
  • Received by editor(s): January 26, 2004
  • Published electronically: December 12, 2005
  • © Copyright 2005 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 19 (2006), 327-344
  • MSC (2000): Primary 32G15; Secondary 14D07
  • DOI: https://doi.org/10.1090/S0894-0347-05-00512-6
  • MathSciNet review: 2188128