
BaselDijonEPFL seminar
Basel, November 2930, 2021
Schedule
In Vesalianum  Kleiner Hörsaal (O1.13), Vesalgasse 1, 4051 Basel
Monday
November 29

Tuesday
November 30


9h1510h15 Benoît Cadorel Complex hyperbolicity, VHS and Higgs bundles
10h4511h45 Andriy Regeta When is the automorphism group of an affine variety nested?
12h0013h00 PierreMarie Poloni
Real forms of affine algebraic varieties: two examples

lunch 
lunch 
14h0015h00 Alan Muniz
Symmetries of foliations on surfaces
15h3016h30 Sokratis Zikas Rigid birational involutions of ℙ3
17h0018h00 Fabio Bernasconi
On the log liftability of Fsplit surfaces
social dinner


Fabio Bernasconi (EPFL)  On the log liftability of Fsplit surfaces
Given a projective variety X over an algebraically closed field of characteristic p>0, it is an interesting question to understand
the possible geometric and arithmetic obstruction for the existence of a lifting to characteristic zero.
In this direction, motivated
by the case of abelian varieties and K3 surfaces, it is
conjectured that ordinary
CalabiYau varieties
should admit a lifting to characteristic zero.
In this talk I will report a joint work with I. Brivio, T. Kawakami
and J. Witaszek where we show that globally Fsplit
surfaces (which can be thought as arithmetically wellbehaved log CalabiYau pairs) are log liftable to characteristic zero.
As a corollary we deduce the Bogomolov bound on the number of
singular points of Fsplit klt del Pezzo surfaces (which was known to be false without the Fsplitness
condition).

Benoît Cadorel (Nancy)  Complex hyperbolicity, VHS and Higgs bundles
Given a complex projective manifold of general type X, it is in general a very difficult problem to determine the locus of its entire curves, that is, the images of holomorphic maps from the complex plane with values in X. If this locus is not Zariski dense, we say that X is quasihyperbolic. The GreenGriffithsLang conjecture then states that for projective manifolds, this property should be equivalent to being of general type; this remains a widely open question in general.
The previous conjecture has been a guiding question for many moduli problems for which the parameter spaces is known to have negative curvature properties. This has lead to an important amount of work in the last few years (starting with Griffiths, Schmid, Viehweg, Zuo... and more recently with Brunebarbe, Rousseau, Deng, Brotbek,...), and has permitted to obtain strong hyperbolicity results for many interesting classes of varieties, in particular the ones supporting variations of Hodge structures (VHS). In this talk, I will present a recent work with Y. Deng, where we prove hyperbolicity properties of varieties supporting a nilpotent harmonic Higgs bundle, which form a natural generalization of VHS.

Alan Muniz (Dijon)  Symmetries of foliations on surfaces
Let X be a smooth complex projective surface. A foliation F on X is given by a subsheaf of the tangent sheaf, TF > TX. Under some positivity condition on TF* we have finiteness for the group Aut(F) of automorphisms of X that preserve F. In this talk we will address the problem of bounding the order of Aut(F).
Under mild conditions on X and F we will show that Aut(F) is bounded above by a degree 3 polynomial on the Chern numbers of F and X. This is done by analysing invariant loci for subgroups of Aut(F). We will also prove, via a slightly different approach, a linear bound for foliations on the projective plane X = P2. This talk is based on joint works with Mauricio Corrêa and Rudy Rosas.

PierreMarie Poloni (Basel)  Real forms of affine algebraic varieties: two examples
We will show that the famous Russell cubic threefold admits a unique isomorphism class of real forms and that all surfaces of equation xy=p(z) (often called Danielewski surfaces) admit at most six isomorphism classes of real forms.
This is joint work with Jérémy Blanc and Anna Bot

Andriy Regeta (Jena)  When is the automorphism group of an affine variety nested?
In this talk we will discuss the structure of the automorphism group of an affine variety.
More precisely, we conjecture that the following conditions on the neutral component of the automorphism group are equivalent:
(1) it is equal to the union of all algebraic subgroups;
(2) it is exhausted by an inductive limit of algebraic subgroups (then we call it nested);
(3) it is a semidirect product of an algebraic torus and a direct limit of abelian unipotent algebraic groups;
(4) its unipotent elements comprise an abelian subgroup.
This conjecture holds in dimension 2 and partially in arbitrary dimension: the equivalences hold for a subgroup of the automorphism group generated by connected algebraic subgroups.
This talk is based on the joint work with Alexander Perepechko.

Sokratis Zikas (Basel)  Rigid birational involutions of ℙ3
The Cremona group is the group of birational transformations of the projective nspace over some field k.
The study of these groups dates back to the 19th century with some of the central questions still being open.
In the recent years new techniques, based on the Minimal Model Program, have been developed to answer some of these questions over the field of complex numbers.
In this talk, using these techniques, I will explain how to construct families of birational involutions on the projective 3space which do not fit in an elementary relation of Sarkisov links.
Using these involutions, we can construct new homomorphisms from the Cremona group, effectively reproving nonsimplicity, and show that it admits a free product structure.
Finally, using the free product structure, we will show that the group of automorphisms of the Cremona group is not generated by inner and field automorphisms.


Participants
Ahmed Abouelsaad (Basel)
Jefferson Baudin (EPFL)
Vladimiro Benedetti (Dijon)
Fabio Bernasconi (EPFL)
Jérémy Blanc (Basel)
Anna Bot (Basel)
Benoît Cadorel (Nancy)
JungKyu Canci (Basel)
Adrien Dubouloz (Dijon)
Mani Esna Ashari (Basel)
Daniele Faenzi (Dijon)
Stefano Filipazzi (EPFL)
Pascal Fong (Basel)
PierreAlexandre Gillard (Dijon)
Tanuj Gomez (Freiburg)
Hanspeter Kraft (Basel)
Philipp Mekler (Basel)
Alan Muniz (Dijon)
Irène Meunier (Basel)
PierreMarie Poloni (Basel)
Quentin Posva (EPFL)
Andriy Regeta (Jena)
Javier Carvajal Rojas (EPFL)
Roberto Svaldi (EPFL)
Ronan Terpereau (Dijon)
Christian Urech (EPFL)
Immanuel Van Santen (Basel)
Sokratis Zikas (Basel)
Send an email to Jeremy Blanc unibas ch if you would like to participate.
Organisers
Jérémy Blanc (Basel)
Adrien Dubouloz (Dijon)
Christian Urech (EPFL)
Roberto Svaldi (EPFL)
Ronan Terpereau (Dijon)
