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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Global rigidity of the period mapping

Author: Benson Farb
Journal: J. Algebraic Geom.
Published electronically: October 24, 2022
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Abstract | References | Additional Information

Abstract: Let ${\mathcal M}_{g,n}$ denote the moduli space of smooth, genus $g\geq 1$ curves with $n\geq 0$ marked points. Let ${\mathcal A}_h$ denote the moduli space of $h$-dimensional, principally polarized abelian varieties. Let $g\geq 3$ and $h\leq g$. If $F:{\mathcal M}_{g,n} \to {\mathcal A}_H$ is a nonholomorphic map, then $h=g$ and $F$ is the classical period mapping, assigning to a Riemann surface $X$ its Jacobian.

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Additional Information

Benson Farb
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
MR Author ID: 329207

Received by editor(s): June 26, 2021
Received by editor(s) in revised form: March 13, 2022
Published electronically: October 24, 2022
Additional Notes: This work was supported in part by National Science Foundation Grant No. DMS-181772, the Eckhardt Faculty Fund, and the Jump Trading Mathlab Research Fund
Article copyright: © Copyright 2022 University Press, Inc.