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Algebraic Geometry conference - Basel
Basel, December 18-20, 2023
Schedule
Monday
December 18
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Tuesday
December 19
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Wednesday
December 20
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Kollegienhaus 116
09h30-10h20
Pascal Fong
Automorphisms of ℙ1-bundles over ruled surfaces
10h30-11h20
Anna Bot
Survey on real forms
11h40-12h30
Maxim Amirkhanov
Finite birational actions on non-trivial Severi-Brauer surfaces
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Kollegienhaus 117
09h30-10h20
Erik Paemurru
Restrictions of toric weighted blowups
10h30-11h20
Ronan Terpereau
Homogeneous instanton bundles on Fano threefolds
11h40-12h30
Fabio Bernasconi
Sarkisov program for surfaces over arbitrary fields
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| lunch |
lunch |
lunch |
Kollegienhaus 115
13h50-14h40
Andrea Fanelli
Maximal connected algebraic subgroups of Cremona groups
15h00-15h50
Hamid Abban
Introduction to K-stability
Spiegelgasse 1, 6th floor
coffee/tea break
Spiegelgasse 5 - Seminarraum 05.002
16h50-17h40
Christian Urech
Automorphisms of plane Cremona groups revisited
social dinner |
Kollegienhaus 116
13h50-14h40
Egor Yasinsky
Finite groups of birational self-maps
15h00-15h50
Immanuel van Santen
On the Manin-Mumford theorem for Algebraic Groups
Spiegelgasse 1, 6th floor
coffee/tea break
Spiegelgasse 5 - Seminarraum 05.001
16h50-17h40
Beamer-Karaoke
social dinner
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Hamid Abban (Nottingham) - Introduction to K-stability
I will give a very introductory and friendly talk about K-stability, explaining why it is important (for algebraic geometers and non-algebraic geometers), how it is verified that a Fano is K-stable, and give plenty of examples and open problems.
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Maxim Amirkhanov (Basel) - Finite birational actions on non-trivial Severi-Brauer surfaces
We'll discuss ongoing work of Jérémy Blanc and the speaker on the possible finite subgroups of the group of birational automorphisms of a non-trivial Severi-Brauer surface over a perfect field, generalizing the characteristic 0 case, in which a classification of such subgroups was given by Constantin Shramov recently.
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Fabio Bernasconi (Basel) - Sarkisov program for surfaces over arbitrary fields
The Sarkisov program is a powerful tool to decompose birational maps of Mori fibre spaces.
Using the excellent MMP of Tanaka, we prove the Sarkisov programme for surfaces over arbitrary, possibly imperfect, fields.
This allows to extend several results of the Italian and Russian schools on del Pezzo surfaces and conic bundles to arbitrary fields.
I will illustrate the results with tons of examples and show how to overcome the lack of Galois theory methods.
This is joint with A. Fanelli, J. Schneider and S. Zimmermann
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Anna Bot (Basel) - Survey on real forms
A real form of a complex scheme is a real scheme whose complexification is isomorphic to . In the last few years, there has been considerable progress in the understanding of how many nonisomorphic real forms a given complex variety can have. In the projective case, a variety can have at most countably many nonisomorphic real forms, where Lesieutre found the first example with infinitely many, and Dinh, Oguiso and Yu found a rational surface with infinitely many. No such restriction on the cardinality exists for affine or quasi-projective varieties, with examples of surfaces having uncountably many nonisomorphic real forms constructed recently. In fact, in the known examples, the real forms can be parametrised by a variety, where one has to be careful in formulating this intuitive notion. In this talk, I will survey the known results about real forms and discuss some open problems.
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Andrea Fanelli (Bordeaux) - Maximal connected algebraic subgroups of Cremona groups
Ten years ago, Jérémy Blanc and Jean-Philippe Furter proved that the Cremona group of rank n≥2 cannot be endowed with the structure of an (ind-)algebraic group. Since then, several people - you may know few of them! - developed new approaches to study maximal algebraic subgroups of the Cremona groups, via modern birational geometry.
In this talk I will survey the recent progress in this field and present a joint project with Enrica Floris and Susanna Zimmermann, showing how the existence of stably rational non-rational varieties is deeply related to maximal connected algebraic subgroups of the Cremona group.
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Pascal Fong (Paris-Saclay) - Automorphisms of ℙ1-bundles over ruled surfaces
The classification of algebraic subgroups of groups of birational transformations has been initiated by Enriques and Fano. Over the field of complex numbers, they stated the classification of connected algebraic subgroups of Bir(ℙ3), but the complete proof of their classification was given later by Umemura. Using only algebraic technics, Blanc, Fanelli and Terpereau recover most of the cases of this classification and their results hold over any algebraically closed field of characteristic zero. Following the strategy and the ideas developed by Blanc, Fanelli and Terpereau, we classify pairs (X,Aut°(X)) where X is the total space of a ℙ1-bundle over a ruled surface and Aut°(X) is a maximal connected algebraic subgroup of Bir(X/S).
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Erik Paemurru (Saarbrücken) - Restrictions of toric weighted blowups
Kawakita 2001 proved that 3-dimensional divisorial contractions with centre a smooth point are (1, a, b)-blowups. Boissière-Floris 2021 gave a 4-dimensional example of a divisorial contraction with centre a curve which is not a (a, b, c, d)-blowup. In this talk, I give simple examples of divisorial contractions in dimension n > 3 that are not (w1, ..., wn)-blowups where the centre has dimension less than (n-1)/2. In the second part of the talk I prove that blowups of hypersurfaces in projective space along hypersurfaces in lower-dimensional projective spaces are Mori dream spaces, I describe their Mori chamber decomposition and the associated birational models, which is a joint work with T. Guerreiro and L. Campo.
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Ronan Terpereau (Lille) - Homogeneous instanton bundles on Fano threefolds
An instanton bundle on the projective space is a stable rank 2 vector bundle with zero first Chern class and which satisfies a certain cohomological vanishing condition. Instanton bundles originally appeared in the 1970s in Yang-Mills theories (a family of theories used to describe fundamental force fields in physics), but they have since attracted much attention from the mathematical community ; in particular, for questions related to the geometry of their moduli spaces. The notion of instanton bundle was extended in the early 2010s to certain Fano threefolds by Daniele Faenzi and Alexander Kuznetsov. In this talk, we will be interested in G-homogeneous (i.e. invariant for the action of an algebraic group G) instanton bundles on Fano varieties of Picard number 1 when G acts with an open orbit. This is a joint work with Daniele Faenzi.
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Christian Urech (Basel) - Automorphisms of plane Cremona groups revisited
A theorem of Déserti states that all group automorphisms of the plane Cremona group as well as the group of polynomial automorphisms of the affine plane are inner up to field automorphisms. However, her proof requires that the base-field is uncountable. In this talk, I will give new proofs of these results and explain how to generalize them to many other base-fields. We will also see that for certain base fields the statement is no longer true. This is work in progress with Jeanette Fernandez.
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Immanuel van Santen (Basel) - On the Manin-Mumford theorem for Algebraic Groups
A classical version of the Manin-Mumford theorem (proven by Raynaud) states the following: Let G be an abelian variety and let X be a subset of G such that the torsion points X_tor lie dense in X. Then the closure of X is equal to a connected closed subgroup up to a torsion element. Later this theorem was generalized to commutative connected algebraic groups by Hindry.
In this talk we discuss a generalization of this statement to arbitrary connected algebraic groups. This is joint work with Harry Schmidt.
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Egor Yasinsky (Bordeaux) - Finite groups of birational self-maps
I will give an overview of recent progress in classification of finite groups acting on rationally connected varieties.
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Participants
Hamid Abban (Nottingham)
Ahmed Abouelsaad (Basel)
Maxim Amirkhanov (Basel)
Fabio Bernasconi (Basel)
Jérémy Blanc (Basel)
Anna Bot (Basel)
Jung-Kyu Canci (Basel)
Mani Esna Ashari (Basel)
Andrea Fanelli (Bordeaux)
Enrica Floris (Poitiers)
Pascal Fong (Paris-Saclay)
Jean-Philippe Furter (Bordeaux)
Maria Fernanda Graf (Basel)
Isac Héden (Uppsala)
Mattias Hemmig (Basel)
Irène Meunier (Toulouse)
Erik Paemurru (Saarbrücken)
Pierre-Marie Poloni (Basel)
Anne Schnattinger (Basel)
Julia Schneider (Zürich)
Aline Sprunger (Basel)
Ronan Terpereau (Lille)
Christian Urech (Basel)
Immanuel Van Santen (Basel)
Henrik Wehrheim (Basel)
Egor Yasinsky (Bordeaux)
Sokratis Zikas (Poitiers)
Susanna Zimmermann (Paris-Saclay)
Organiser
Jérémy Blanc (Basel)
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