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North German Algebraic Geometry Seminar
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Thursday 29.11.2007 (lecture hall 1101-F428) |
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| 14:30 - 15:30 h | Hans-Christian v. Bothmer | Indices of vector fields on complete intersection singularities |
| 15:30 - 16:00 h | Coffee break | |
| 16:00 - 17:00 h | Christian Curilla | Arithmetic intersection numbers of Fermat curves |
| 17:15 - 17:45 h | Informal Discussion: Future of the North German Algebraic Geometry Seminar | |
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Friday 30.11.2007 (lecture hall 1101-F428) |
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| 09:30 - 10:30 h | Stefan Wewers | Die arithmetische Fundamentalgruppe und Diophantische Geometrie |
| 10:30 - 11:00 h | Coffee break | |
| 11:00 - 12:00 h | Michael Stoll | Statistics on rational points on small genus 2 curves |
| 12:00 - 14:00 h | Lunch break (Restaurant 'Cum Tempore' on Campus) | |
| 14:00 - 15:00 h | Björn Andreas | Stable vector bundles on K3 fibrations |
| 15:00 - 15:30 h | Coffee break | |
| 15:30 - 16:30 h | Filippo Viviani | Cohomological support loci for Abel-Prym curves |
| 16:30 - 17:00 h | Coffee Break | |
| 17:00 - 18:00 h | Gavril Farkas | Maps between moduli spaces of curves and Gieseker-Petri divisors |
Abstracts
Stable vector bundles on K3 fibrationsBjörn Andreas (Freie Universität Berlin)
Abstract: The search for constructions of stable vector bundles and their moduli spaces on Calabi-Yau manifolds has been motivated by questions from string theory and higher dimensional gauge theory. We use the theory of Fourier-Mukai transforms to construct moduli spaces of stable sheaves (and bundles) on K3-fibered Calabi-Yau threefolds. As an application, the bundles provide new examples of heterotic string vacua.
Indices of vector fields on complete intersection singularities
Hans-Christian Graf von Bothmer (Leibniz-Universität Hannover, currently Universität Göttingen)
Abstract: Let X be a complex analytic vector field with an isolated zero P on a complex variety V. If V is smooth at P, the index of X at P is a topological invariant that can be defined either as the degree of a certain map or algebraically as the dimension of a certain algebra. Both definitions agree by a local version of the Poincaré-Hopf Theorem. In this talk I will explain how the geometric and the algebraic approach have been generalized to deal with singular varieties, and show how W. Ebeling, X. Gómez-Mont and I proved recently that both generalizations agree for locally complete intersection varieties.
Arithmetic intersection numbers of Fermat curves
Christian Curilla (Universität Hamburg)
Abstract: only available as PDF
Maps between moduli spaces of curves and Gieseker-Petri divisors
Gavril Farkas (Humboldt-Universität Berlin)
Abstract: We study contractions of the moduli space of stable curves beyond the minimal model of Mg by resolving and giving a complete enumerative description of the rational map between two moduli spaces of curves Mg --> Mh which associates to a curve of genus , the Brill-Noether locus of special divisors in the case this locus is a curve. As an application we construct many examples of moving effective divisors on of small slope. For low , our calculation can be used to study the intersection theory of the moduli space of Prym varieties of dimension 5.
Statistics on rational points on small genus 2 curves
Michael Stoll (Jacobs-Universität Bremen)
Abstract: I will report on computations I have done recently, trying to find all rational points (at least up to very large height) on all genus 2 curves that have a model of the form
Cohomological support loci for Abel-Prym curves
Filippo Viviani (Humboldt-Universität Berlin)
Abstract: Cohomological support loci were introduced by Green-Lazarsfeld to prove some generic vanishing theorems for irregular varieties. Recently, Pareschi-Popa studied the cohomological support loci of subvarieties of minimal cohomological class inside a principal polarized abelian variety. In particular, they obtained a new cohomological characterization of Abel-Jacobi curves. In this talk, based on a joint work with S. Casalaina-Martin and M. Lahoz, we consider the analougous problem for the "next class of curves", namely Abel-Prym curves inside Prym varieties.
Die arithmetische Fundamentalgruppe und Diophantische Geometrie
Stefan Wewers (Leibniz-Universität Hannover)
Abstract:
Lecture hall 1101-F428:
Building 1101 is the main building of Leibniz-Universität Hannover, the Welfenschloß, tram-stop 'University'.The easiest way to find the lecture hall is the following: Entering the building by the main entrance, cross the main hall and turn left. After the first glass door turn left again (before reaching the second glass door) to find the elevator, which takes you to 4th floor in close proximity of the lecture hall.
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