Titles

Ekaterina Amerik: Sur une description de courbes extrémales sur les variétés hyperkaehleriennes de type K3

Marcello Bernardara: Fano varieties of K3 type and where to find them - part 2

Michele Bolognesi: Espaces de modules de cubiques de dimension 4 et motifs de type abélien

Ana-Maria Castravet: Effective cones of divisors on moduli spaces of stable rational curves

Thomas Dedieu: On the automorphism of Mukai varieties - part 1

Daniele Faenzi: Again on Fano threefolds of genus 10 and Coble cubics

Enrico Fatighenti: Fano varieties of K3 type and where to find them - part 1

Lie Fu: Fano varieties, hyperkahler varieties, and the Franchetta property - part 2

Alexander Kuznetsov: Smooth hyperplane sections of the Cayley plane

Robert Laterveer: Fano varieties, hyperkahler varieties, and the Franchetta property - part 1

Laurent Manivel: On the automorphism of Mukai varieties - part 2

Nicolas Perrin: Cohomology of general hyperplane sections of (co)adjoint varieties

Some abstracts

Michele Bolognesi: Espaces de modules de cubiques de dimension 4 et motifs de type abélien

Dans cet exposé nous étudierons la théorie d'intersection des diviseurs des cubiques spéciales dans l'espace de modules de hypersurfaces cubiques de dimension 4. Nous allons donner des conditions nécessaires pour que (jusqu'à) 20 diviseurs s'intersectent, et nous allons décrire les K3 associées à ces cubiques. Nous allons appliquer cette construction pour construire des nouvelles familles de cubiques avec motif de Chow de dimension finie et de type abélien. Enfin nous allons considérer certaines variétés de HyperKähler associées aux cubiques (la variétés de Fano des droites, le LLSvS 8fold, etc.) et nous allons montrer que dans certains cas nos résultats nous permettent de montrer que ces variétés HK ont aussi motif de Chow de dimension fini.

Daniele Faenzi: Again on Fano threefolds of genus 10 and Coble cubics

We describe the fibre of the period map of Fano threefolds of genus 10 as an open subset of the Coble-Dolgachev sextic. I will try to focus on the "Torelli" part, namely how to recover the threefold from a hyperplane dual to the Coble cubic, or equivalently from its Hilbert scheme of lines.

Lie Fu, Robert Laterveer: Fano varieties, hyperkahler varieties, and the Franchetta property

A family of varieties has the Franchetta property if for every element of the family, the generically defined part of the Chow ring injects into cohomology. We will introduce this notion, and give a panoramic overview of known results and open questions related to Fano varieties of K3 type and hyperkaehler varieties.

Nicolas Perrin: Cohomology of general hyperplane sections of (co)adjoint varieties

(ongoing j.w. V. Benedetti) For X = G/P in P(V) a rational projective homogeneous space embedded in the projective space of some G-representation V, we consider general hyperplane sections Y = X \cap (h = 0). Our first result is a classification all pairs (X,V) such that, for h general, Y is stable under the action of a maximal torus of G.

Our second result is a formula for computing the T-equivariant cohomology of Y = X \cap (h = 0) for such a pair (X,V). We also compute the middle intersection form in terms of the Cartan matrix of the root system. We also use the quantum cohomology of X to obtain information on the quantum cohomology of Y.