On the geometry of the second fundamental form of the Torelli map
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- by Paola Frediani and Gian Pietro Pirola
- Proc. Amer. Math. Soc. 149 (2021), 1011-1024
- DOI: https://doi.org/10.1090/proc/15291
- Published electronically: January 13, 2021
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Abstract:
In this paper we give a geometric interpretation of the second fundamental form of the period map of curves and we use it to improve the upper bounds on the dimension of a totally geodesic subvariety $Y$ of $\mathsf {A}_g$ generically contained in the Torelli locus obtained by Elisabetta Colombo, Paola Frediani, and Alessandro Ghigi [Internat. J. Math. 26 (2015), no. 1, 1550005] and A. Ghigi, P. Pirola, and S. Torelli (to appear on Communications in Contemporary Mathematics, https:// doi.org/10.1142/S0219199720500200). We get $\dim Y \leq 2g-1$ if $g$ is even, $\dim Y \leq 2g$ if $g$ is odd. We also study totally geodesic subvarieties $Z$ of $\mathsf {A}_g$ generically contained in the hyperelliptic Torelli locus and we show that $\dim Z \leq g+1$.References
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Bibliographic Information
- Paola Frediani
- Affiliation: Dipartimento di Matematica “Felice Casorati”, Università di Pavia, Italy
- MR Author ID: 347739
- ORCID: 0000-0003-2537-2727
- Email: paola.frediani@unipv.it
- Gian Pietro Pirola
- Affiliation: Dipartimento di Matematica “Felice Casorati”, Università di Pavia, Italy
- MR Author ID: 139965
- Email: gianpietro.pirola@unipv.it
- Received by editor(s): September 12, 2019
- Received by editor(s) in revised form: July 2, 2020
- Published electronically: January 13, 2021
- Additional Notes: The authors are members of GNSAGA of INdAM. The authors were partially supported by national MIUR funds, PRIN 2017 Moduli and Lie theory, and by MIUR: Dipartimenti di Eccellenza Program (2018-2022) - Dept. of Math. Univ. of Pavia.
- Communicated by: Matthew A. Papanikolas
- © Copyright 2021 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 149 (2021), 1011-1024
- MSC (2010): Primary 14H10, 14H15, 14H40, 32G20
- DOI: https://doi.org/10.1090/proc/15291
- MathSciNet review: 4211858