This is the homepage of a 2-day conference in Nijmegen on arithmetic geometry. The conference starts on Wednesday September 23rd and ends on Thursday September 24th with the PhD defense of Finn Bartsch. The schedule is below; note that the room changes with every session.
Speakers: Daniel Greb, Frederic Campana, Damian Brotbek, Erwan Rousseau, Claire Voisin
Titles and abstracts below
Wednesday 10h-10:30h: Welcome
Room: Just outside of the room LIN2 in the Linnaeus building
Wednesday 10:30h - 11:30h: Erwan Rousseau
Room: LIN2 (Linnaeus building)
Wednesday 12h - 13h : Daniel Greb
Room: LIN2 (Linnaeus building)
Wednesday 13h-15h: lunch break
Wednesday 15h-15:30h: coffee
Room: Just outside of HG00.308 in Huygensgebouw
Wednesday 15:30h-16:30h: Damian Brotbek
Room: HG00.308 (Huygensgebouw)
Wednesday 17h-18h: Frederic Campana
Room: HG00.308 (Huygensgebouw)
Thursday 10h-1030h: Coffee
Room: Just outside of HG00.307 (Huygensgebouw)
Thursday 1030h-1130h: Claire Voisin
Room: HG00.307 (Huygensgebouw)
11:30h : Walk towards de Aula. Small lunch is served there. This is a 15 minute walk approximately.
12:30h : PhD defense Finn Bartsch
Location: De Aula
Damian Brotbek
Title:
Abstract:
Frederic Campana
Title:
Abstract:
Daniel Greb
Title: Arakelov inequalities and characterisation of totally geodesic ball quotients
Abstract: I will talk about joint work with Carolina Tamborini and Matteo Costantini, in which we establish an Arakelov inequality for variations of Hodge structures underlying families of principally polarised complex Abelian varieties. In the equality case, this leads to a numerical characterisation of certain totally geodesic ball quotients inside the moduli space of Abelian varieties. Our result extends work of Möller-Viehweg-Zuo by removing the strong positivity conditions on the log-canonical and the log-cotangent bundle imposed in their statement. For families over compact base spaces, our proof involves showing in a first step that the period map associated with a family of Abelian varieties factors through certain operations of the MMP and then generalising the results of Möller, Viehweg, and Zuo to the resulting singular setting. In the quasiprojective case, we develop a new approach and execute it in dimension two: it first descends the family to a very specific partially ample model and then uses symmetric space theory and semistability considerations to detect totally geodesic ball quotients in the moduli space considered with the locally symmetric orbifold Kähler metric.
Erwan Rousseau
Title
Abstract:
Claire Voisin
Title: On the Chow ring of very general abelian varieties and a question of Pirola
Abstract: On the moduli space of genus 4 curves, there is a rational section of the Kummer fibration (that is, the Jacobian fibration mod. +- Id) given by the difference of the two trigonal divisors. We prove that any rational section of the Kummer fibration is a multiple of this section, solving in the affirmative a question asked by Pirola. A first step for the proof is a result concerning the Chow ring of a very general abelian variety A of dimension at least 4, or very general Jacobian A in genus at least 4 . We prove that a divisor D on A that satisfies $D2=0$ in $CH2(A)$ must be of torsion.