Oberseminar Algebraische und Arithmetische Geometrie
Das Oberseminar findet meist donnerstags von 16:30 Uhr bis 18 Uhr im Raum g117 oder f309 (*) statt.
Außerdem lassen sich die Oberseminartermine vergangener Semester abfragen.
10. Oktober (10:00-12:00)
On Zariski Decomposition With and Without Support
3-dimensional Frobenius manifolds via elliptic curves
Abstract We investigate 3-dimensional Frobenius manifolds that appear as the subvarieties in the deformation space of simple elliptic singularities. We set up the connection between such Frobenius manifolds and elliptic curves. With the help of elliptic curves theory we give the classification of such Frobenius manifolds having additional symmetries and defined over Q.
On quartic surfaces with many lines.
Abstract We show that a smooth quartic surface over algebraically closed field of characteristic different from 2,3 contains at most 64 lines. We discuss properties of quartics with lines of the second kind (joint work with Prof. M. Schuett (LU Hannover).
Interpolation problems in P^n
Abstract We give an overview of interpolation problems in P^n. We investigate the speciality of effective linear systems in P^n with assigned multiple points and linear base locus. For this, we compute the cohomology groups of the strict transforms of divisors via the blow-up of their linear base locus. (with C. Brambilla and E. Postinghel) We extend this computations to non-effective divisors in P^n. In particular this shows that linear cycles are special effect varieties for effective linear systems interpolating points. Using the birational geometry of Cremona transformantion we give new classes of special effect varieties of dimension 1 and 2 in P4. (with R. Miranda) This generalizes the elemetary (-1) curves of Laface-Ugalia in P 3, and it also give information on the Effective cone of the Blown up P 4 in arbitrary number of points.
14. November (16:00-17:00)
Algebraic geometric Codes and Lattices
Abstract We will give a short overwiew of codes and lattices and their connections. Then we want to construct codes and lattices from function fields of algebraic curves over finite fields. We fix a finite set of points. The code constructions are on the one hand evaluations of a linear system related to a divisor and on the other hand residues of linear systems of differentials. The lattice construction is related to lattices of units from number fields and makes use of principal divisors. In the end we will find a connection between this algebraic-geometric codes and lattices.
Discrete derived categories
Abstract Discrete derived categories, as defined by Vossieck, form a class of triangulated categories which are sufficiently simple to make explicit computation possible, but also non-trivial enough to manifest interesting behaviour. In this seminar, I will explain what they are, and talk about some recent work with D. Pauksztello and D. Ploog, where we study the autoequivalences and bounded t-structures on these categories. I will go on to describe work in progress, aiming to understand the corresponding spaces of Bridgeland stability conditions.
Christian Böhning (Hamburg)
Rationality problems: a bird's eye view
Abstract After a general introduction to and sample of guiding open
Miguel Angel Marco Buzunariz
Euler characteristic, counting polynomial and Chern-Schwarz-MacPherson class of an algebraic set
Abstract Deducing the topology of an algebraic set from its defining equations is, in general, a difficult task. In this talk, a method to compute the Euler characteristic will be presented. Using the same method it is possible to compute a stronger invariant, that is directly related to the Chern-Schwarz-MacPherson class. We will also show how this stronger invariant is related to the problem of counting points of varieties over finite fields.
Daniel Greb (Bochum)
Construction and variation of moduli spaces of sheaves on higher-dimensional base manifolds
Abstract While the variation of moduli spaces of H-slope/Gieseker-semistable sheaves on surfaces under change of the ample polarisation H is well-understood, research on the corresponding question in the case of higher-dimensional base manifolds revealed a number of pathologies. After presenting these, I will discuss recent joint work with Matei Toma (Nancy) and Julius Ross (Cambridge) which resolves some of these pathologies by looking at curves instead of divisors, and by embedding the moduli problem for sheaves into a moduli problem for quiver representations.
Gunther Cornelissen (Utrecht)