On Picard bundles over Prym varieties

  1. Brambila-Paz, L. 3
  2. E. Gómez-González 1
  3. Pioli, F. 2
  1. 1 Departamento de Matemáticas, Universidad de Salamanca
  2. 2 Dipartimento di Matematica, Università degli Studi di Genova
  3. 3 CIMAT, México
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Revista:
Collectanea mathematica

ISSN: 0010-0757

Any de publicació: 2001

Volum: 52

Fascicle: 2

Pàgines: 157-168

Tipus: Article

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Altres publicacions en: Collectanea mathematica

Resum

Let $\pi: Y\rightarrow X$ be a covering between non-singular irreducible projective curves. The Jacobian $J(Y )$ has two natural subvarieties, namely, the Prym variety $P$ and the variety $\pi^\ast(J(X))$. We prove that the restriction of the Picard bundle to the subvariety $\pi^\ast(J(X))$ is stable. Moreover, if $\widetilde P$ is a principally polarized Prym- Tyurin variety associated with $P$, we prove that the induced Abel-Prym morphism $\widetilde p: Y\rightarrow\widetilde P$ is birational to its image for genus $g_X > 2$ and deg $\pi\not= 2$. We use this result to prove that the Picard bundle over the Prym variety is simple and moreover is stable when $\widetilde p$ is not birational onto its image.

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