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In this short note, we study the Jacobian variety of the Accola-Maclachlan curve of genus four and obtain explicitly its Poincaré isogeny decomposition. More precisely, we show that its Jacobian variety is isomorphic to the product of two abelian surfaces that are simple, and provide explicitly a Riemann matrix for each one of the involved Abelian surfaces.

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On the Jacobian Variety of the Accola-Maclachlan Curve of Genus Four

  • 会议论文

  • 发表日期：

    2025年

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  • Robert Auffarth,
  • Sebastián Reyes-Carocca,
  • Anita M. Rojas

摘要

In this short note, we study the Jacobian variety of the Accola-Maclachlan curve of genus four and obtain explicitly its Poincaré isogeny decomposition. More precisely, we show that its Jacobian variety is isomorphic to the product of two abelian surfaces that are simple, and provide explicitly a Riemann matrix for each one of the involved Abelian surfaces.