A remark on a Nagell-Lutz type statement for the Jacobian of a curve of genus 2 and a (2, 3, 6) quasi-torus decomposition of a sextic with 9 cusps

Hiro-o Tokunaga; Yukihiro Uchida

arxiv: 1808.10187 · v2 · pith:OJTQUL2Fnew · submitted 2018-08-30 · 🧮 math.AG · math.NT

A remark on a Nagell-Lutz type statement for the Jacobian of a curve of genus 2 and a (2, 3, 6) quasi-torus decomposition of a sextic with 9 cusps

Hiro-o Tokunaga , Yukihiro Uchida This is my paper

classification 🧮 math.AG math.NT

keywords curvedecompositiongenusjacobiannagell-lutzquasi-torusstatementanalogous

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In this note, an analogous statement to the Nagell-Lutz theorem does not hold for the Jacobian of a certain curve of genus 2 over $\mathbb{C}(t)$. As a by-product, we give a (2, 3, 6) quasi-torus decomposition for the dual curve of a smooth cubic.

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A remark on a Nagell-Lutz type statement for the Jacobian of a curve of genus 2 and a (2, 3, 6) quasi-torus decomposition of a sextic with 9 cusps

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