Location: GA 3 21 at the Bernoulli Center (click on the number of the room for a map)
Schedule:
3 April
14:00-15:00 Marc Abboud (Neuchâtel)
Title: A bound on the action of nilpotent groups on complex algebraic varieties
Abstract: We discuss the following result. If G is a finitely generated nilpotent group acting faithfully on a complex algebraic variety X, then the dimension of X is larger than the virtual derived length of G, i.e the minimum of the derived length of the finite index subgroup of G. The proof uses p-adic analysis and p-adic Lie groups method. We show that up to finite index there exists a prime p such that G acts analytically on a p-adic manifold related to X. The study of this action gives the desired bound.
15:00-15:30 break
15:30-16:30 Lyalya Guseva (Dijon)
Title: Full exceptional collections on Isotropic Grassmannians
Abstract: The bounded derived category of coherent sheaves D(X) is an important invariant of an algebraic variety X. While the structure of derived categories is generally quite intricate, in certain cases when D(X) admits a so-called full exceptional collection, D(X) can be described explicitly. Some of the earliest examples of full exceptional collections were constructed by Kapranov in 1983 for classical Grassmannians. Since then, a folklore conjecture says that full exceptional collections consisting of vector bundles exist in the derived categories of all rational homogeneous varieties. In my talk I will outline the proof of this conjecture for all rational homogeneous varieties associated with symplectic groups.
This is joint work with Sasha Novikov.
16:30-17:00 break
17:00-18:00 Luca Tasin (Milano Statale)
Title: Positivity of Hodge bundles and applications
Abstract: Given a fibration f:X→T, positivity properties of the direct image of relative pluricanonical sheaves are important in moduli theory and birational geometry. I will present several positivity results under the assumption that f is a stable family. If time permits, I will also discuss applications to the theory of foliations.
19:00 Dinner
4 April
9:00-10:00 Antoine Pinardin (Edinburgh)
Title: Linearization problem for finite subgroups of the plane Cremona group
Abstract: The plane Cremona group is the group of birational self-maps of the projective plane. Over the field of complex numbers, its subgroups have been extensively studied, and the most complete classification dates back to 2006, with the work of Dolgachev and Iskovskikh. The authors point out a list of questions yet to be answered. The first and main open problem they outline consists in describing the linearizable subgroups of the plane Cremona group, namely those which are conjugated to a subgroup of linear automorphisms of the projective plane. This problem is of particular importance, because it is equivalent to the question of G-equivariant rationality. We give a complete answer to the problem over an algebraically closed field of characteristic 0.
This talk is based on joint work with Arman Sarikyan and Egor Yasinsky.
10:00-10:15 break
10:15-11:15 Niklas Müller (Duisburg-Essen)
Title: Minimal Projective Varieties satisfying 3c2 = c12
Abstract: It is a classical fact that the Chern classes of any minimal smooth projective surface X satisfy the so-called Bogomolov-Miyaoka-Yau inequality 3c2(X)-c12(X) ≥ 0 and it is known explicitly for which surfaces equality is attained. More generally, if X is a minimal projective variety of dimension n, Miyaoka proved that (3c2(X)-c12(X))Hn−2 ≥ 0 for any ample divisor H on X. In this talk I want to discuss the structure of those varieties X attaining equality. In particular, we will see that abundance holds for such varieties.
This is joint work with M. Iwai and S.-i. Matsumura.
11:15-11:30 break
11:30-12:30 Eduardo Alves da Silva (Basel)
Title: Algebraic tori in the complement of quartic surfaces
Abstract: Log Calabi-Yau pairs can be thought of as generalizations of Calabi-Yau varieties. Previously, Ducat showed that all coregularity 0 log Calabi-Yau pairs (P3,B) are crepant birational to a toric model. A stronger condition to consider is whether the complement of B contains a dense algebraic torus. When this is the case, we say that the pair (P3,B) is of cluster type. In this talk, we will show a complete classification of coregularity 0, semi-log canonical (slc), reducible quartic surfaces whose complements contain a dense algebraic torus. As part of this discussion, we will explore the concept of relative cluster type pairs. Finally, we will share some partial results concerning the case of irreducible quartic surfaces.
This work is based on joint research with Fernando Figueroa and Joaquín Moraga.
12:30-14:00 lunch
14:00-15:00 Aline Zanardini (EPFL)
Title: GIT for linear systems of hypersurfaces
Abstract: In this talk, we will consider the problem of classifying linear systems of hypersurfaces inside projective space and up to projective equivalence. I will report on a possible approach to solving this problem via geometric invariant theory, and I will further illustrate how such an approach can be applied to some relevant geometric examples.
This is based on joint work with Masafumi Hattori.