seminario Ritzenthaler
C. Ritzenthaler (Marsiglia) parlera' su
"Serre obstruction for genus 3 curves"
"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."