Lundi 18 janvier 2010
IRMA
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.
Conference web site here
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Lundi 18 janvier 2010
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10:30 - 11:30
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\Deltaas pairs of the LMMPbut with addtional invariantsmorphisms,...)In this categoryone can introduce the notion of 'orbifold rational curves'Athough the properties are expected to be the same as in the usual case where \Delta=0the proofs do not seem to apply directly (for exampleMiyaoka-Mori Bend-and-Break does not always apply)and some technics or ideas seem to be needed. -
11:45 - 12:45
Viktoria Heu, Strasbourg
Isomonodromic deformations and maximally stable bundles
We are interested in holomorphic rank 2 vector bundles of degree 0 over compact Riemann surfaceswhich are provided with irreducible meromorphic connectionsIn the case of a logarithmic connection on the Riemann spheresuch a vector bundle is trivial up to a small move of the polesaccording to a result of ABolibrukhIn the general case of meromorphic connections over Riemann surfaces of arbitrary genuswe prove that the vector bundle is semi-stable (and even maximally stableup to a small isomonodromic deformation. -
14:30 - 15:30
Philipp Habegger, Zurich
Torsion Points on Fibered Powers of an Elliptic Surface
Consider a family of abelian varieties whose base is an algebraic varietyThe union of all torsion groups over all fibers of the family will be called the set of torsion points of the familyIf the base variety is a point then the family is just an abelian varietyIn this case the Manin-Mumford Conjecturea theorem of Raynaudimplies 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 subvarietyThis talk is on possible extensions to certain families where the base is a curveConjectures of Andrand Pink then suggest considering "special points"these are torsion points whose corresponding fibers satisfy an additional arithmetic propertyOne possible property is for the fiber to have complex multiplicationanother is for the fiber to be isogenous to an abelian variety fixed in advanceWe discuss some new results on the distribution of such "special pointson the subvarieties of the family and the role of height functions in their proofs. -
16:00 - 17:00
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 coversThe situation in positive characteristic is much more subtleI will describe and compare two approaches for a group of degree pone using cyclotomic covers of twisted stable curves (joint work with Olsson and Vistoliand one using variable group schemes (joint work in progress with Romagny).