On Picard bundles over Prym varieties

• L. Brambila-Paz ^[3] ; E. Gómez-González ^[1] ; F. Pioli ^[2]
  1. [1] Universidad de Salamanca

     Universidad de Salamanca

     Salamanca, España

     
  2. [2] University of Genoa

     University of Genoa

     Genoa, Italia

     
  3. [3] Mathematics Research Center

     Mathematics Research Center

     México

     

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 52, Fasc. 2, 2001, págs. 157-168
• Idioma: inglés
• Títulos paralelos:
  • Fibrados de Picard sobre variedades de Prym
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• Resumen

  • 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.