About the Seminar

The "Joint Seminar in Algebraic and Complex Geometry" is a research seminar, organized by the research groups in Freiburg, Nancy and Strasbourg. The seminar meets roughly twice per semester in Strasbourg, for a full day. There are about four talks per meeting, both by invited guests and by speakers from the organizing universities. We aim to leave ample room for discussions and for a friendly chat.

The talks are open for everyone. Contact one of the organizers if you are interested in attending the meeting. We have some (very limited) funds that might help to support travel for some junior participants.

Next Meeting

Date

The next meeting is scheduled for January 18, 2009. The meeting will start at 10:30.

Speakers

  • Frédéric Campana (Nancy): Orbifold rational curves and classification theory
    The birational classification of complex projective manifolds needs to work in the slightly larger category of 'geometric orbifolds' (same objects (X, \Delta) as pairs of the LMMP, but with addtional invariants, morphisms,...). In this category, one can introduce the notion of 'orbifold rational curves'. Athough the properties are expected to be the same as in the usual case where \Delta=0, the proofs do not seem to apply directly (for example, Miyaoka-Mori Bend-and-Break does not always apply), and some technics or ideas seem to be needed.

  • Dan Abramovich (Providence): Degree-p Galois covers and their degenerations
    A smooth proper moduli stack of Galois covers of stable curves in characteristic 0 is provided by admissible covers. The situation in positive characteristic is much more subtle. I will describe and compare two approaches for a group of degree p: one using cyclotomic covers of twisted stable curves (joint work with Olsson and Vistoli) and one using variable group schemes (joint work in progress with Romagny).

  • Philipp Habegger: Torsion Points on Fibered Powers of an Elliptic Surface

    Consider a family of abelian varieties whose base is an algebraic variety. The union of all torsion groups over all fibers of the family will be called the set of torsion points of the family. If the base variety is a point then the family is just an abelian variety. In this case the Manin-Mumford Conjecture, a theorem of Raynaud, implies that a subvariety of the abelian variety contains a Zariski dense set of torsion points if and only if it is itself essentially an abelian subvariety. This talk is on possible extensions to certain families where the base is a curve. Conjectures of André and Pink then suggest considering "special points": these are torsion points whose corresponding fibers satisfy an additional arithmetic property. One possible property is for the fiber to have complex multiplication; another is for the fiber to be isogenous to an abelian variety fixed in advance. We discuss some new results on the distribution of such "special points" on the subvarieties of the family and the role of height functions in their proofs.

  • Viktoria Heu (Strasbourg): Isomonodromic deformations and maximally stable bundles
    We are interested in holomorphic rank 2 vector bundles of degree 0 over compact Riemann surfaces, which are provided with irreducible meromorphic connections. In the case of a logarithmic connection on the Riemann sphere, such a vector bundle is trivial up to a small move of the poles, according to a result of A. Bolibrukh. In the general case of meromorphic connections over Riemann surfaces of arbitrary genus, we prove that the vector bundle is semi-stable (and even maximally stable) up to a small isomonodromic deformation.

Schedule

10:30-11:30
 Talk: Campana
11:40-12:40
 Talk: Heu

* Lunch Break *
14:30-15:30
 Talk: Habegger
16:00-17:00
 Talk: Abramovich

Venue

Institut de Recherche Mathématique Avancée
7 rue René Descartes
67084 Strasbourg Cedex

 Salle de seminaire 309

A description of the way is found here.

Mailing List

The meetings of the seminar will be announced via a mailing list. To subscribe, simply send an e-mail to seminar-nfs-subscribe@math.uni-freiburg.de.