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On the group algebra decomposition of a Jacobian variety

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

Given a compact Riemann surface X with an action of a finite group G, the group algebra \(\mathbb Q[G]\) provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely build a decomposition of this kind. Our method allows us to study the geometry of the decomposition. For instance, we build several decompositions in order to determine which one has kernel of smallest order. We apply this method to families of trigonal curves up to genus 10.

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Acknowledgments

This article is part of my Ph.D. thesis written under the direction of Professor Anita Rojas at the Universidad de Chile. I am very grateful to Professor Rojas for sharing, patiently and kindly, her knowledge, experiences and advice. I would like to thank Professors A. Carocca, R. Rodríguez for helpful advice and questions, and M. Izquierdo, who helped me to present this work. I also express my acknowledgments to Linkoping University, where the final version of this paper was written.

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  1. Leslie Jimenez

    Present address: Linköpings universitet, 581 83, Linköping, Sweden

Authors and Affiliations

  1. Departamento de Matemáticas, Facultad de Ciancias, Universidad de Chile, Las palmeras, 3425, Santiago, Ñuñoa, Chile

    Leslie Jimenez

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  1. Leslie Jimenez
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Correspondence to Leslie Jimenez.

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Partially supported by Fondecyt Grant 1100113 and Conicyt Fellowship for Ph.D. studies.

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Jimenez, L. On the group algebra decomposition of a Jacobian variety. RACSAM 110, 185–199 (2016). https://doi.org/10.1007/s13398-015-0226-6

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  • DOI: https://doi.org/10.1007/s13398-015-0226-6

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