Lundi 18 octobre 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.
Lieu : salle de conférences IRMA
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Lundi 18 octobre 2010
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10:30 - 11:30
Alex Küronya, Freiburg/Budapest
Okounkov bodies and transcendental numbers
By looking at orders of vanishing along certain subvarietiesone can associate a convex body to every big divisor on a projective varietyits so-called Okounkov bodyThe construction comes originally from Okounkovand was later vastly generalized by Lazarsfeld and Mustata. The Euclidean dimension of these convex bodies is independent of the specified subvarietiesand measures the asymptotic growth of the number of global sectionswhich is also called the volume of the given divisorIn this talkwe will be primarily be interested with the arithmetic properties of volumes. As it turns outon curves and surfaces the volume of a divisor is always rationalCutkosky showed twenty years ago that there are algebraic numbers that show up as volumes of divisorsIt has been unknown until recently whether one can find divisors with transcendental volumesfor which we will provide an example. This is an account of joint work with Victor Lozovanu and Catriona Maclean. -
11:45 - 12:45
Ann Lemahieu, Freiburg/Lille
The monodromy conjecture for nondegenerate surface singularities.
The monodromy conjecture predicts a relation between the geometry and the topology of singularitiesIn particularit says that a pole s_0 of the local topological zeta function in 0 associated to a hypersurface induces an eigenvalue of monodromy e^{2i pi s_0at a point of the hypersurface in the neighbourhood of 0When the singularity is given by a polynomial that is nondegenerate with respect to its Newton polyhedronthen one can express the local topological zeta function and the zeta function of monodromy in terms of the Newton polyhedronWe analyze these formulas for surface singularitieswe provide a set of monodromy eigenvalues and a set of false candidate polesIn this way we obtain a proof for the monodromy conjecture for nondegenerate surface singularities. -
14:30 - 15:30
Erwan Rousseau, IRMA
Higher dimensional tautological inequalities and applications
We study the degeneracy of holomorphic mappings tangent to holomorphic foliations on projective manifoldsUsing Ahlfors currents in higher dimensionwe obtain several degeneracy statementsJoint work with CGasbarri and GPacienza. -
16:00 - 17:00
Matei Toma, Nancy
On the Kaehler rank of compact complex surfaces
The Kaehler rank of compact complex surfaces was introduced by Harvey and Lawson in their 1983 paper on Kähler manifolds as a measure of (non-)kählerianityIt was not clear though whether the Kaehler rank was a birational invariantThe purpose of this talk is to show that it is oneThis will follow from a partial classification of surfaces of Kähler rank 1.