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Algebraic geometry
A non-hyperelliptic curve with torsion Ceresa class
Arnaud Beauville1 
1 Université Côte d’Azur, CNRS – Laboratoire J.-A. Dieudonné, Parc Valrose, F-06108 Nice cedex 2, France.
Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 871-872.

We exhibit a non-hyperelliptic curve C of genus 3 such that the class of the Ceresa cycle [C]-[-C] in the intermediate Jacobian of JC is torsion.

Received:
Accepted:
Published online:
DOI: 10.5802/crmath.226

Arnaud Beauville 1

1 Université Côte d’Azur, CNRS – Laboratoire J.-A. Dieudonné, Parc Valrose, F-06108 Nice cedex 2, France.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Arnaud Beauville. A non-hyperelliptic curve with torsion Ceresa class. Comptes Rendus. Mathématique, Volume 359 (2021) no. 7, pp. 871-872. doi : 10.5802/crmath.226. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.226/

[1] Dean Bisogno; Wanlin Li; Daniel Litt; Padmavathi Srinivasan Group-theoretic Johnson classes and non-hyperelliptic curves with torsion Ceresa class (2020) (https://arxiv.org/abs/2004.06146)

[2] Giuseppe Ceresa C is not algebraically equivalent to C - in its Jacobian, Ann. Math., Volume 117 (1983) no. 2, pp. 285-291 | DOI | MR | Zbl

[3] Lie Fu; Robert Laterveer; Charles Vial Multiplicative Chow–Künneth decompositions and varieties of cohomological K3 type, Ann. Mat. Pura Appl. (4), Volume 200 (2021) no. 5, pp. 2085-2126 | Zbl

[4] Noriyuki Otsubo On the Abel–Jacobi maps of Fermat Jacobians, Math. Z., Volume 270 (2012) no. 1-2, pp. 423-444 | DOI | MR | Zbl

[5] Yuuki Tadokoro A nontrivial algebraic cycle in the Jacobian variety of the Klein quartic, Math. Z., Volume 260 (2008) no. 2, pp. 265-275 | DOI | MR | Zbl

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