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New sextics of genus 6 and 10 attaining the Serre bound

  • Annamaria Iezzi , Motoko Qiu Kawakita and Marco Timpanella EMAIL logo
Published/Copyright: January 24, 2024
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Abstract

We provide new examples of curves of genus 6 or 10 attaining the Serre bound. They all belong to the family of sextics introduced in [19] as a generalization of Wiman’s sextics [38] and Edge’s sextics [9]. Our approach is based on a theorem by Kani and Rosen which allows, under certain assumptions, to fully decompose the Jacobian of the curve. With our investigation we are able to update several entries in the table www.manypoints.org, see [37].

  1. Communicated by: G. Korchmáros

Acknowledgements:

This research was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA - INdAM). The first author is funded by the European Union - FSEREACT-EU, PON Research and Innovation 2014-2020 DM1062/2021 contract number 18-I-15358-2. The second author is funded by JSPS Grant-in-Aid for Scientific Research (C) 17K05344. The third author is funded by the project “Metodi matematici per la firma digitale ed il cloud computing" (Programma Operativo Nazionale (PON) “Ricerca e Innovazione" 2014-2020, University of Perugia).

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Received: 2023-05-02
Revised: 2023-09-22
Published Online: 2024-01-24
Published in Print: 2024-01-29

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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