The fibers of the ramified Prym map
P. Frediani, J.C. Naranjo, I. Spelta

TL;DR
This paper investigates the fibers of the ramified Prym map, providing geometric descriptions in specific cases and presenting an explicit example of a totally geodesic curve within a fiber.
Contribution
It offers a detailed geometric analysis of the generic fibers of the ramified Prym map in six special cases and constructs an explicit example of a totally geodesic curve as a Prym fiber component.
Findings
Geometric description of generic fibers in six special cases.
Explicit example of a totally geodesic curve as a Prym fiber component.
Analysis of the dimension discrepancy between source and target spaces.
Abstract
We study the ramified Prym map which assigns to a ramified double cover of a smooth irreducible curve of genus ramified in points the Prym variety of the covering. We focus on the six cases where the dimension of the source is strictly greater than the dimension of the target giving a geometric description of the generic fibre. We also give an explicit example of a totally geodesic curve which is an irreducible component of a fibre of the Prym map .
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