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2 results

  • Generic Torelli theorem for Prym varieties of ramified coverings

  • Part of
  • Valeria Ornella Marcucci, Gian Pietro Pirola
  • Journal:
    Compositio Mathematica / Volume 148 / Issue 4 / July 2012
    Published online by Cambridge University Press:
    11 July 2012, pp. 1147-1170
    Print publication:
    July 2012
    • Article
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  • We consider the Prym map from the space of double coverings of a curve of genus g with r branch points to the moduli space of abelian varieties. We prove that 𝒫:ℛg,r→𝒜δg−1+r/2 is generically injective if We also show that a very general Prym variety of dimension at least 4 is not isogenous to a Jacobian.

  • SCHOTTKY UNIFORMIZATIONS OF GENUS 3 AND 4 REFLECTING ${\mathcal S}_{4}$

  • RUBÉN A. HIDALGO
  • Journal:
    Journal of the London Mathematical Society / Volume 72 / Issue 1 / August 2005
    Published online by Cambridge University Press:
    20 July 2005, pp. 185-204
    Print publication:
    August 2005

  • Schottky uniformizations are provided of every closed Riemann surface $S$ of genus $g \in \{3,4\}$ admitting the symmetric group ${\mathcal S}_{4}$ as group of conformal automorphisms. These Schottky uniformizations reflect the group ${\mathcal S}_{4}$ and permit concrete representations of ${\mathcal S}_{4}$ to be obtained in the respective symplectic group $\mbox{Sp}_{g}({\mathbb Z})$. Their corresponding fixed points, in the Siegel space, give principally polarized Abelian varieties of dimension $g$. For $g=3$ and for some cases of $g=4$ they turn out to be holomorphically equivalent to the product of elliptic curves.