Seminari di Geometria Algebrica a.a. 2012-2013

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25 febbraio 2013, ore 15:30, sala conferenze Tricerri
Sukmoon Huh (Korea Institute for Advanced Studies) Globally generated vector bundles on a smooth quadric threefold
ABSTRACT. Globally generated vector bundles are basic objects in projective algebraic geometry and they correspond to morphisms to Grassmannian varieties. Recently there have been several works on the classification of globally generated vector bundles on projective spaces. In this talk, we classify globally generated vector bundles with very low first Chern class on a smooth quadric threefold, starting with the rank 2 case to even higher rank. And we also investigate their indecomposability. Main ingredients are the Liaison and the technique of smoothing algebraic curves on a quadric threefold. This is joint work with E. Ballico and F. Malaspina.
4 dicembre 2012, ore 16:00, sala conferenze Tricerri
C. Ritzenthaler (UniversitÓ di Marsiglia) Serre obstruction for genus 3 curves
ABSTRACT. Let k be a field. A principally polarized abelian variety (A,a) over k, which is a Jacobian over \bar{k} is not necessarily a Jacobian over k. Serre pointed out that there may be an obstruction and asked how it could be computed. For abelian threefolds, we gave two characterizations of this obstruction. The first one in terms of a Siegel modular form which is, over the complex, the product of the 36 even Thetanullwerte; the second one which is purely geometric and related to Recillas trigonal construction. I will review some aspects of these works. More recently, a new surprising phenomena has appeared in experiments when one let the abelian threefold vary over a given finite field. In order to perform these experiments, one has to deal with the explicit problem of spanning the moduli space of smooth plane quartics. Several attempts to do this efficiently will be proposed.

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