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Singularities of theta divisors and the geometry of 𝒜 5

Gavril Farkas, Samuele Grushevsky, Salvati R. Manni, Alessandro Verra (2014)

Journal of the European Mathematical Society

We study the codimension two locus H in 𝒜 g consisting of principally polarized abelian varieties whose theta divisor has a singularity that is not an ordinary double point. We compute the class [ H ] C H 2 ( 𝒜 g ) for every g . For g = 4 , this turns out to be the locus of Jacobians with a vanishing theta-null. For g = 5 , via the Prym map we show that H 𝒜 5 has two components, both unirational, which we describe completely. We then determine the slope of the effective cone of 𝒜 5 ¯ and show that the component N 0 ' ¯ of the Andreotti-Mayer...

Sur l’espace de modules des faisceaux semi stables de rang 2, de classes de Chern (0,3) sur 2

K. Hulek, Joseph Le Potier (1989)

Annales de l'institut Fourier

L’espace de modules M = M ( 0 , 3 ) des faisceaux semi-stables de rang 2, de classes de Chern (0,3) sur le plan projectif 2 est une variété projective irréductible et lisse de dimension 9. Dans M , les points qui ne proviennent pas d’un faisceau localement libre constituent une hypersurface M . Dans cet article, nous montrons que toute surface complété de M rencontre la frontière M , autrement dit qu’il n’existe pas de famille de fibrés vectoriels paramétrée par une surface complète de M . La démonstration repose...

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