Prym varieties that are not isomorphic to Jacobian

preprint2026arXivOpen access

Abstract

We study Prym varieties of ramified (at precisely two points) double covers of smooth irreducible complex projectives curves that admit an automorphism of prime order p>2p>2. Using Galois theory, we give an explicit constructions of Prym varieties that are not isomorphic to jacobians (even if one ignores the polarizations).

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