Lundi 14 mars 2011

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.

Lieu : salle de conférences IRMA

  • Lundi 14 mars 2011

  • 10:30 - 11:30

    Fundamental groups of special threefolds

    — Benoît Claudon (Nancy)

    Special manifolds form a class of varieties which share many of the properties of manifolds with non positive canonical bundle and these manifolds are actually built up from two types of geometry : RC varieties and manifolds with trivial canonical bundle. In particular, their fundamental groups should be virtually abelian. We prove this fact for Kähler threefolds using tools such as orbifolds metrics and Log-MMP of surfaces. This is joint work with F. Campana.
  • 11:45 - 12:45

    Algebraic varieties with quasi-projective universal cover

    — Andreas Höring (Freiburg/Paris)

    Assuming the abundance conjecture, we prove that the universal cover of a normal, projective variety X is quasi-projective if and only if a finite, étale cover of X is a fiber bundle over an Abelian variety with simply connected fiber. This is joint work with B. Claudon and J. Kollár.
  • 14:30 - 15:30

    A new look at Drinfeld p-adic upper half plane

    — Michael Rapoport (Bonn)

    Drinfeld a donne une identification du demi-plan attache a un corps local p-adique comme solution d'un probleme de modules, en montrant qu'il represente le foncteur des groupes p-divisibles munies d'une action "speciale" de l'anneau des entiers du corps des quaternions. Dans cet expose je montre qu'il y a egalement une interpretation par un autre probleme de modules de groupes p-divisibles (travail commun avec Kudla).
  • 16:00 - 17:00

    F-singularities and alterations

    — Manuel Blickle (Mainz)

    (joint with Karl Schwede and Kevin Tucker) One of the main tools in the birational classifiacation of varieties over a field of characteristic zero are multiplier ideal sheaves and related invariants of singularities. Geometrically these are defined via resolutions of singularities. In positive characteristic there is a parallel theory of so called test ideals whose definition does not rely on resolution of singularities but instead uses the Frobenius. Starting from observations about the transformation behaviour under birational and finite maps I will introduce a description of an ideal which in equal characteristic zero yields the multiplier ideal, and in positive characteristic the test ideal. As an application we obtain a geometric characterization of F-rational singularities and a Nadel-type vanishing theorem in positive characteristic.