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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...

Stability of pencils of plane quartic curves

Edoardo Ballico, Paolo Oliverio (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota si danno dei criteri per la stabilità di fasci di quartiche piane.

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