Basel-Dijon-EPFL meeting (7-8 Nov 2019)

Location: CH B3 31 for all talks except the last one, which is in MA A3 30 ( click on the number of the room for a map)

Schedule:

7 Nov

14:00-15:00 Calum Spicer

Tilte: Mori theory and foliations

Abstract: We will explain some of the ideas behind the study of the birational geometry of foliations, as well as indicating some recent progress in the case of codimension one foliations on threefolds. Features joint work with P. Cascini and R. Svaldi.

15:00-15:30 coffee

15:30-16:30 Emelie Arvidsson

Title: Kodaira type vanishing theorems on log del Pezzo surfaces of fixed index in positive characteristic

Abstract: Abstract: I will discuss Kodaira vanishing theorem on a log del Pezzo surface of fixed Gorenstien index over an algebraically closed field of positive characteristic. By a result of of Cascini, Tanaka and Witaszek Kodaira vanishing holds on such surfaces provided that the characteristic of the base field is sufficiently large. I will present a bound on the characteristic of the base field for which this vanishing may fail in terms of the index. As a consequence, we show that Kodaira vanishing theorem holds on a Gorenstein del Pezzo surface over an algebraically closed field of characteristic greater than or equal to 9221. 

16:30-17:00 coffee

17:00-18:00 Egor Yasinsky

Title: Birational automorphisms of del Pezzo fibrations

Abstract: We study groups of birational automorphisms of 3-dimensional del Pezzo fibrations using the Sarkisov program. After explaining main ideas, I will focus on the case of cubic del Pezzo fibrations X. We shall construct some non-trivial homomorphism from Bir(X) to a free product of infinitely many groups of order 2. As an application, we will see that in the Cremona group of rank 3, all connected algebraic subgroups generate a proper normal subgroup. Joint work with J. Blanc.

19:00 Dinner

8 Nov

9:00-9:15 coffee

9:15-10:15 Roberto Diaz

Title: Action of the additive group on affine ind-varieties

Abstract: Let V be an affine algebraic variety on C and O(V ) its ring of regular functions, a known result is the correspondence between actions of the additive group Ga = (C, +) on V and locally nilpotent derivations on O(V ). In this talk I will describe a generalization of this correspondence to the category of affine ind-varieties.

10:15-10:30 coffee

10:30-11:30 Stéphane Druel

Title: On foliations with semi-positive anti-canonical bundle

Abstract: I will discuss the structure of (regular) foliations with semi-positive anti-canonical bundle on complex projective manifolds. I will also describe the (mostly conjectural) structure of foliations with numerically trivial canonical class.

11:30-11:45 coffee

11:45-12:45 Ulrike Riess

Title: Base loci of big and nef line bundles on irreducible symplectic varieties

Abstract: In the first part of this talk, I give a complete description of the divisorial part of the base locus of big and nef line bundles on irreducible symplectic varieties (under certain conditions). This is a generalization of well-known results of Mayer and Saint-Donat for K3 surfaces. In the second part, I will present what is currently known on the non-divisorial part.

12:45- 14:15 Lunch

14:15-15:15 Yohan Brunebarbe

Title: Algebraicity of period maps via o-minimal geometry

Abstract: In this talk I will introduce o-minimal geometry and illustrate its relevance to proving algebraicity of certain analytically defined objects. As an application, I will explain that the period maps associated to variations of pure Hodge structures are algebraic in corestriction to their image, as conjectured by Griffiths. This is joint work with Benjamin Bakker and Jacob Tsimerman.