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10h30-11h30 - Damian BROTBEK - 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 X 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.
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11h45-12h45 - Clemens JOERDER -
On the Poincaré lemma on singular spaces |
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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.
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14h30-15h30 - Sergei KOVALENKO - Smooth Non-Homogeneous Gizatullin Surfaces |
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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 [Ko], 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.
[Ko] S. Kovalenko, Transitivity of automorphism groups of Gizatullin surfaces, arXiv: 1304.7116.
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16h-17h - Giovanni MONGARDI - Ample cone and negative divisors for Hilbert schemes of points on K3s |
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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. |