Oberseminar Geometrie & Topologie

Die Vortäge im Oberseminar Geometrie & Topologie werden auf den Seiten des SFB 701 angekündigt.

A superficial afternoon

There will be a small workshop focusing mainly on the theory of algebraic surfaces.

Sönke Rollenske and Michael Lönne
Date & Location
6 December 2013 (Nikolaus) in V3-201, Bielefeld University (directions)
If you want to attend, please send an email to zaeper@math.uni-bielefeld.de . We can reimbourse travel costs (up to a certain limit).
10:00 Tea
11:35 Nicolas Perrin: Quantum K-Theory of homogeneous spaces
Quantum K-Theory is a generalisation of both quantum cohomology and K-theory. We shall explain how rational connectedness results on certain varieties of curves in a homogeneous space X imply finiteness or positivity results in the quantum K-theory QK(X) of X. (j.w. Buch, Chaput and Mihalcea).
ca. 12:45 Lunch break
14:00 Roberto Pignatelli: On fibred surfaces of general type
A standard approach to many questions in algebraic geometry, as classification questions, is (roughly speaking) to restrict to a subvariety (mainly ample divisors or fibres of morphisms), which has smaller dimension and then is simpler to study, and then deduce the result on the whole variety. A very typical example is the crucial role played by fibrations in the classification of algebraic surfaces. I will concentrate on the case of the surfaces of general type, discussing some classical result and some more recent application.
15:00 Tea
15:30 Amir Dzambic: Some geometric applications of quaternionic Shimura varieties
We use the term "quaternionic Shimura variety" to denote a quotient of the product of n copies of the complex upper half plane by an arithmetic lattice in PSL2(R)^n. The most famous examples of such varieties are Hilbert modular varieties which are well studied from both the arithmetic and geometric point of view. Less is known when one considers quaternionic Shimura variety defined by a cocompact arithmetic lattice. After a general discussion of quaternionic Shimura varieties, I would like to present how quaternionic Shimura varieties can be used to construct varieties of general type with "interesting" numerical invariants including fake quadrics and their higher dimensional generalizations as well as other surfaces of general type and geometric genus zero. Furthermore I would like to address some interesting open questions related to such constructions. This is partially a joint work with X.Roulleau (Poitiers).