Practical

The session took place on Thursday June 5 2025 at the University of Strasbourg, Salle de conférence (ground floor)

The address is:

IRMA - Université de Strasbourg
Salle de conférence (ground floor)
10, rue du Général Zimmer
67000 Strasbourg, France

Schedule

10:30–12:00	Gianluca Pacienza: Recent progress on the Morrison-Kawamata cone conjecture
12:00–13:30	lunch
13:30–14:30	Daniele Agostini: Coble duality for Jacobian Kummer fourfolds
14:30–15:00	coffee break
15:00–16:00	Massimiliano Alessandro: On the birationality of the pluricanonical maps of some 3-folds of general type

We intend to always feature one (longer) talk of a more survey-ish nature in each session.

Speakers, titles and abstracts

Gianluca Pacienza: Recent progress on the Morrison-Kawamata cone conjecture

Many properties of a projective algebraic variety can be encoded by convex cones, such as the ample cone and the cone of curves. This is especially useful when these cones have only finitely many edges, as happens for Fano varieties. The Morrison-Kawamata cone conjecture predicts the structure of these cones, in terms of the action of groups of transformations, even for classes of varieties for which these cones may be round or have infinitely many edges. In the talk, I will try to explain the relevance of the conjecture within the framework of the MMP, present its different variants, and give an overview of some of the most recent results.

Daniele Agostini: Coble duality for Jacobian Kummer fourfolds

The Coble cubic of a Jacobian abelian surface A is the unique cubic which is singular along A in its natural embedding in P^8. We show how to use this cubic to build a duality between two birational models of the Kummer fourfold of A. Along the way, we also construct a non-natural automorphism on the Hilbert square of A. This is joint work with Pietro Beri, Franco Giovenzana and Angel Rios.

Massimiliano Alessandro: On the birationality of the pluricanonical maps of some 3-folds of general type

In 2017 Catanese provided a representation-theory-based criterion to ensure that the canonical map phi of a smooth complex algebraic variety X of general type is birational under the assumption that there exists a Galois cover X->Y. In a joint work in progress with Christian Gleissner we adapt this criterion to 3-folds isogeneous to a product of curves via an abelian group and generalize it to pluricanonical maps. We also provide an effective construction method which leads us to explicit examples of 3-folds where phi is birational.