Serre-Tate lifts for Calabi-Yau varieties
Friday, 28.10.11, 10:00-11:00, Raum 404, Eckerstr. 1
For an ordinary Abelian variety over a perfect field of\npositive characteristic, Serre and Tate discovered a\ncanonical lift over the Witt ring. Later, this has been\ngeneralized to varieties with trivial tangent bundles by\nNori and Srinivas. In this talk, we will construct a\ncanonical lift for ordinary varieties with trivial\ncanonical sheaves, which generalizes Serre-Tate as well as\nNori-Srinivas. As applications, we obtain a Serre-Tate\ntheory for Calabi-Yau varieties (as anticipated by\nStienstra), as well as a Bogomolov-Tian-Todorov\nunobstructedness theorem for such varieties (building on\nwork of Ekedahl and Shepherd-Barron). We also discuss\nexamples due to Hirokado, Schroeer, Schoen, Cynk and van\nStraten of non-liftable Calabi-Yau varieties for which\nunobstructedness of deformations fails.\n
Nori-Motive und Tannaka-Kategorien
Friday, 4.11.11, 10:00-11:00, Raum 404, Eckerstr. 1
Universelle Konstruktionen von Nori-Motive
Friday, 4.11.11, 10:00-11:00, Raum 404, Eckerstr. 1
Compact moduli spaces of surfaces via MMP
Friday, 25.11.11, 10:00-11:00, Raum 404, Eckerstr. 1
Relative version of the Kontsevich-Zagier conjecture on periods.
Friday, 2.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
We formulate and prove a relative version of the K-Z conjecture on periods. In this relative version, numbers (and rational numbers) will be replaced by Laurent series (and rational functions).
Negative curves on algebraic surfaces
Friday, 9.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
It has been a long-standing folklore conjecture going back to Enriques, that on a smooth projective surface over the complex numbers the self-intersection of curves has a lower bound. \n\nIn a joint work with Bauer, Harbourne, Knutsen, Müller-Stach, and Szemberg, we disprove the conjecture with the help of certain Hilbert modular surfaces.
Vorstellungsvortrag
Friday, 16.12.11, 10:00-11:00, Raum 404, Eckerstr. 1
Pencils of cubic fourfolds
Friday, 20.1.12, 10:00-11:00, Raum 404, Eckerstr. 1
We will discuss some Hodge-theoretic aspects of families of cubic fourfolds. Our focus will lie on so-called special cubic fourfolds, which contain an algebraic surface not homologous to a plane. We will show that there is a modular form that counts the special members of a pencil of cubic fourfolds. If time permits, we will go on with some speculations on the derived category of special cubic fourfolds and homological mirror symmetry.
Invarianten arithmetischer Gruppen
Friday, 10.2.12, 10:00-11:00, Raum 404, Eckerstr. 1
Koszul-Dualität
Friday, 17.2.12, 10:00-11:00, Raum 404, Eckerstr. 1
Komplexe Multiplikation auf elliptischen Kurven
Tuesday, 27.3.12, 10:15-11:15, Raum 404, Eckerstr. 1
Elliptische Kurven haben sogenannte komplexe Multiplikation, wenn ihr Endomorphismenring nicht nur aus den ueblichen n-Multplikationsabbildungen besteht. Ziel meines Vortrags ist es, einige der grundlegende Eigenschaften sowie den Hauptsatz elliptischer Kurven mit komplexer Multiplikation zu beschreiben, der es ermoeglicht, die Klassenkoerpertheorie eines quadratisch imaginaeren Zahlenkoerpers explizit mit Hilfe der j-Invariante und den Torsionspunkten einer solchen Kurve zu beschreiben. Sofern es die Zeit erlaubt, wuerde ich anschliessend wenigstens auf einige Aspekte des Beweises eingehen und einen Ausblick geben, wie sich die Theorie fuer den Fall abelscher Varietaeten verallgemeinern laesst.