Prym varieties that are not isomorphic to Jacobian
Yuri G. Zarhin

TL;DR
This paper investigates Prym varieties arising from ramified double covers of complex curves with automorphisms of prime order, providing explicit constructions of those not isomorphic to Jacobians.
Contribution
It introduces explicit constructions of Prym varieties that are not isomorphic to Jacobians, expanding understanding of Prym varieties with automorphisms of prime order.
Findings
Constructed examples of Prym varieties not isomorphic to Jacobians
Utilized Galois theory for explicit constructions
Focused on ramified double covers with automorphisms of prime order p>2
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 . 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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Advanced Differential Equations and Dynamical Systems
