Meeting in May 2014

  • Chenyang Xu: Maximal pole of motivic Zeta function. We prove a conjecture of Veys, which says that the opposite of the log canonical threshold is the only possible pole of maximal order of the motivic zeta function over a field of characteristic zero. If time permits, we will also discuss how to apply our method to study a family of Calabi-Yau varieties and prove properties for the weight function associated with a degeneration.(joint with Johannes Nicaise)
  • Tomasz Szemberg: The effect of points fattening. I recall briefly results due to Bocci and Chiantini on the effect of points fattening on the projective plane. Then I will report on some generalizations to other surfaces. The core of the lecture will be devoted to higher dimensional analogies. Results in that part were obtained jointly with Thomas Bauer (Marburg).
  • Olivier Benoist: Complete families of smooth space curves. In this talk, we will study complete families of smooth space curves, that is complete subvarieties of the Hilbert scheme of smooth curves in $\mathbb P^3$. On the one hand, we will construct non-trivial examples of such families. On the other hand, we obtain necessary conditions for a complete family of smooth polarized curves to induce a complete family of non-degenerate smooth space curves. Both results rely on the study of the strong semistability of certain vector bundles.
  • Gianluca Pacienza: Families of rational curves on holomorphic symplectic varieties. I will report on a joint work with François Charles, in which we study families of rational curves on certain irreducible holomorphic symplectic varieties. In particular, we prove that projective holomorphic symplectic fourfolds of (K3)$^{[2]}$-type contain uniruled divisors and rationally connected lagrangian surfaces. I will also mention some applications to the study of Chow groups of such varieties, generalizing analogous results due to Beauville and Voisin on K3 surfaces.