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arXiv · 2205.08522

Jacobians, Anti-affine groups and torsion points

A. J. Parameswaran·Amith Shastri K
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Abstract

We give criteria for the Jacobian of a singular curve $X$ with at most ordinary $n$-point singularities to be anti-affine. In particular, for the case of curves with single ordinary double point we exhibit a relation with torsion divisors. If the geometric genus of the singular curve is atleast 3 and the normalization is non-hyperelliptic and non-bielliptic, then except for finitely many cases the Jacobian of $X$ is anti-affine. Furthermore, if the normalization is a general curve of genus atleast 3 then the Jacobian of $X$ is always anti-affine.

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A. J. Parameswaran, Amith Shastri K. 2022-05-17. Jacobians, Anti-affine groups and torsion points. https://arxiv.org/abs/2205.08522

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