| K. Amerik |
I am going to state the cone conjecture of
Morrison and Kawamata for irreducible holomorphic symplectic
manifolds, recently proved by Misha Verbitsky and myself,
interpret it in terms of hyperbolic geometry and give a few
applications, such as the finiteness of the number of
birational models or the existence of nef line bundles isotropic with respect to the Beauville-Bogomolov form. |
| A.Beauville |
This is a survey of the progress obtained in
the last 10 years on the Chow ring of projective
hyperkäahler manifolds. Starting from the case of K3
surfaces, I will explain why one may hope that this Chow
ring admits a natural grading. While this conjecture seems
inaccessible at the moment, it implies some concrete
consequences on intersections of divisors, which have been
verified in an increasing number of cases. |
| F.Catanese |
I shall report on some particular V(ariations
of) H(odge) S(tructure) coming from integrals on cyclic
coverings of the projective line. The first series leads to
some counterexamples to a question raised by Fujita 30 years
ago about semiampleness of the direct image of the relative
canonical bundle (joint work with Dettweiler). These VHS
come from interesting fibred surfaces, and I shall talk on
work in progress about their geometry. The second one is a
2-parameter VHS leading to a ball quotient S discovered by
Cartwright and Steger via computer calculations, and which
has q=p_g=1. I shall describe the geometrical construction
of S as the covering of a Deligne-Mostow orbifold:
this is joint work with Toledo, Stover and Keum. |
| K. Hulek |
Cubic threefolds have played an important
role in algebraic geometry since Clemens and Griffiths
showed that these are unirational but not rational
varieties. Their proof relies on a careful analysis of the
intermediate Jacobians of cubic threefolds. In this talk I
will discuss how the intermediate Jacobian degenerates when
the cubic threefold takes on singularities such as A_n or
D_n singularities. An important role in this analysis is
played by the Fano surface of lines on cubic threefolds -- a
topic which was also studied by W. Barth and A. Van den Ven.
This is joint work with S. Casalaina-Martin, S. Grushevsky
and R. Laza. |
| C. Peters |
I explain by means of examples the role
of two central themes in van de Ven's work: vector
bundles and complex surfaces. This talk is suited for
mathematicians with little or no background in complex
algebraic geometry. |