We study the ramified Prym map P_{g,r}⟶A^δ_{g−1+r2} which assigns to a ramified double cover of a smooth irreducible curve of genus g ramified in r 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 P_{1,2}.
The fibers of the ramified Prym map
Paola Frediani;Juan Carlos Naranjo;Irene Spelta
2022-01-01
Abstract
We study the ramified Prym map P_{g,r}⟶A^δ_{g−1+r2} which assigns to a ramified double cover of a smooth irreducible curve of genus g ramified in r 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 P_{1,2}.File in questo prodotto:
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