The Torelli map restricted to the hyperelliptic locus
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- by Aaron Landesman;
- Trans. Amer. Math. Soc. Ser. B 8 (2021), 354-378
- DOI: https://doi.org/10.1090/btran/64
- Published electronically: April 9, 2021
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Abstract:
Let $g \geq 2$ and let the Torelli map denote the map sending a genus $g$ curve to its principally polarized Jacobian. We show that the restriction of the Torelli map to the hyperelliptic locus is an immersion in characteristic not $2$. In characteristic $2$, we show the Torelli map restricted to the hyperelliptic locus fails to be an immersion because it is generically inseparable; moreover, the induced map on tangent spaces has kernel of dimension $g-2$ at every point.References
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Bibliographic Information
- Aaron Landesman
- Affiliation: Department of Mathematics, Stanford University, Stanford, California 94305
- MR Author ID: 1178036
- Received by editor(s): February 1, 2020
- Received by editor(s) in revised form: July 15, 2020, July 23, 2020, and November 2, 2020
- Published electronically: April 9, 2021
- Additional Notes: This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1656518.
- © Copyright 2021 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)
- Journal: Trans. Amer. Math. Soc. Ser. B 8 (2021), 354-378
- MSC (2020): Primary 14H40; Secondary 14K10
- DOI: https://doi.org/10.1090/btran/64
- MathSciNet review: 4241766