Mercredi 18 décembre 2013
IRMA
The "Joint Seminar in Algebraic and Complex Geometry" is a research seminar, organized by the research groups in Basel, 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.
The seminar will meet in Strasbourg, December 18th in the conference room of the institute.
Organizer in Strasbourg : G. Pacienza
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Mercredi 18 décembre 2013
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10:30
Damian Brotbek, Strasbourg
Height inequality for surfaces in an abelian variety.
Given a function field K and a projective variety X over K, Vojta conjectured an inequality between the canonical height of an algebraic point on and the discriminant of that point. In this talk, I will explain how to obtain such a height inequality when X is a generic surface in an abelian threefold. The proof if based on the study of higher order jet spaces. This is a joint work with Carlo Gasbarri. -
11:45
Clemens Jörder, Freiburg
On the Poincaré lemma on singular spaces.
On a singular normal complex space the cochain complex of sheaves of reflexive differential forms is not a resolution of the sheaf of locally constant functions, since the Poincaré lemma for reflexive differential forms fails in general. I discuss under which conditions the Poincaré lemma is valid. Furthermore I will relate the question of its failure to vanishing theorems of Kodaira-Akizuki-Nakano type. -
14:30
Sergei Kovalenko, Freiburg
Smooth Non-Homogeneous Gizatullin Surfaces.
Quasi-homogeneous surfaces, or Gizatullin surfaces, are normal affine surfaces such that the complement of the big orbit of the automorphism group is finite. If the action of the automorphism group is transitive, the surface is called homogeneous. Examples of non-homogeneous Gizatullin surfaces were constructed in by the speaker in arXiv:1304.7116, but on more restricted conditions. We show that a similar result holds under less constrained assumptions. Moreover, we exhibit examples of smooth affine surfaces with a non- transitive action of the automorphism group whereas the automorphism group is huge. This means that the automorphism group is not generated by a countable set of algebraic subgroups and that its quotient by the (normal) subgroup, generated by all algebraic subgroups, contains a free group over an uncountable set of generators. -
16:00
Giovanni Mongardi, Bonn
Ample cone and negative divisors for Hilbert schemes of points on K3s.
For K3 surfaces, the ample cone is cut out by rational curves of selfintersection -2. In the case of Hilbert schemes of points of K3 surfaces and their deformations, a similar result can be phrased using certain divisors whose top self intersection is negative.