Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Brill-Noether theory of curves on abelian surfaces

Margherita Lelli-Chiesa

created by daniele on 09 Mar 2015

18 mar 2015 -- 14:30

Aula Riunioni, DM, Pisa

Seminari di Geometria Algebrica, Pisa


Brill-Noether theory of curves on K3 surfaces is well understood. Quite little is known for curves lying on abelian surfaces. Given a general abelian surface S with polarization L of type $(1,n)$, we will first focus on the gonality of smooth curves $C$ in the linear system $
$ and show that this is not constant when moving $C$ in $
$. We will then study linear series of type $g^r_d$ with $r\geq 2$. We will prove that, as soon as the Brill-Noether number is negative and some other inequalities are satisfied, the locus $
^r_d$ of smooth curves in $
$ possessing a $g^r_d$ is nonempty and has the expected dimension. As an application, we obtain the existence of a component of the Brill-Noether locus $M^r_{g,d}$ having the expected codimension in the moduli space of curves $M_g$. This is a joint work with A. L. Knutsen and G. Mongardi.

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