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arXiv · 2412.04940

Pseudoreflections on Prym Varieties

Robert Auffarth·Martí Lahoz·Juan Carlos Naranjo
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Abstract

We show that for every g greater or equal than 5, the locus of Prym varieties in the moduli space of principally polarized abelian varieties of dimension g-1 that possess a pseudoreflection of geometric origin is the union of three different non-empty explicit irreducible families. This is in stark contrast to the loci of Jacobian varieties that possess a pseudoreflection of geometric origin, which is empty for any genus greater than 3. In g=6, a distinguished example of Prym varieties with a pseudoreflection is given by intermediate Jacobians of cubic threefolds that possess an Eckardt point.

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Robert Auffarth, Martí Lahoz, Juan Carlos Naranjo. 2024-12-06. Pseudoreflections on Prym Varieties. https://arxiv.org/abs/2412.04940

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