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arXiv · 1607.08816

Arithmetic invariant theory and 2-descent for plane quartic curves

Jack A. Thorne
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Abstract

Given a smooth plane quartic curve C over a field k of characteristic 0, with Jacobian variety J, and a marked rational point P of C(k), we construct a reductive group G and a G-variety X, together with an injection J(k)/2J(k) -> G(k)\X(k). We do this using the Mumford theta group of J, and a construction of Lurie which passes from Heisenberg groups to Lie algebras.

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Jack A. Thorne. 2016-07-29. Arithmetic invariant theory and 2-descent for plane quartic curves. https://arxiv.org/abs/1607.08816

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