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Basel-Dijon seminar
Basel, April 14-15, 2016
(will be followed by a Dijon-Basel meeting in June (week 6-11) in Dijon).
Schedule
Thursday
April 14
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Friday
April 15
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Spiegelgasse 1 - SR 00.003 (ground floor):
10h15-11h15
Giuseppe Ancona
The Chow ring of a commutative group scheme
11h30-12h30
Adrien Dubouloz
Cylinders in del Pezzo fibrations
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| lunch |
lunch |
Kollegienhaus HS117:
14h00-15h00
Daniele Faenzi
What is a Fano threefold of genus ten ?
15h15-16h15
Gianluca Pacienza
Coisotropic subvarieties of holomorphic symplectic varieties
coffee break (in Spiegelgasse 1)
Spiegelgasse 5 - SR 05.002:
17h00-18h00
Jérémy Blanc
Subvarieties of the Cremona groups
social dinner
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Spiegelgasse 1 - SR 00.003 (ground floor):
14h00-15h00
Jung-Kyu Canci
Scarcity of cycles of rational functions in terms of scarcity of integral points of varieties
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Giuseppe Ancona (Zürich) - The Chow ring of a commutative group scheme.
A classical result of Beauville shows that the action of the multiplication by n on the Chow ring of an abelian variety is semisimple with a finite number of explicit eigenvalues. Beauville's method is based on a Fourier transform using the dual abelian variety.
We will generalize this result to commutative group schemes (semiabelian varieties, Néron models of abelian varieties, mixed Shimura varieties,...). The Fourier transform cannot be generalized to this context, we will show that Voevodsky's motives are a useful tool for this question.
This is a joint work with Annette Huber and Simon Pepin Lehalleur.
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Jérémy Blanc (Basel) - Subvarieties of the Cremona groups
The Cremona groups are the groups of birational transformations of the projective spaces. There is a natural way to define families of birational maps parametrised by algebraic varieties and gives a topology on these groups. If a locally closed subset has a structure of algebraic variety compatible, we will say that this is a subvariety of the Cremona group. In this talk, I will try to explain how to determine which sets are subvarieties and show what kind of pathologies one can find. Joint work with Ivan Pan (Montevideo).
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Jung-Kyu Canci (Basel) - Scarcity of cycles of rational functions in terms of scarcity of integral points of varieties
We will see some recent results contained in a recent work with Salomon Vishkautsan about the cardinality of the set Per(φ;K) of the K-rational periodic points of a rational function φ of degree d>1, defined over a number field K. We prove that the cardinality of the set Per(φ;K) is bounded by an O-big O(d), where the coefficient in the -O-big depends on the places of bad reduction of φ. We prove also that for any finitely generated semigroups I of rational functions of degree bigger than 1, defined over a number field K, there exists a number B=B(I), that depends on I, such that the inequality Per(φ,K) < B holds for each φ∈ I. Note that now the bound B does not depend on the degree of the map φ∈ I. Our result can be seen as application of theorems about the finiteness of integral points in certain varieties.
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Adrien Dubouloz (Dijon) - Cylinders in del Pezzo fibrations
A cylinder in a quasi-projective variety is a Zariski open subset isomorphic to the product of a quasi-projective variety with an affine space of positive dimension. Every smooth del Pezzo surface over an algebraically closed field of characteristic zero contains a cylinder, in fact each point of such a surface admits an open neighborhood isomorphic to the affine plane. The question becomes more subtle when the base field is no longer assumed to be algebraically closed. In this talk, I will mostly address the case of minimal del Pezzo surfaces, with application to the construction of cylinders inside total spaces of higher dimensional del Pezzo fibrations. (Joint work in progress with T. Kishimoto, Saitama University).
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Daniele Faenzi (Dijon) - What is a Fano threefold of genus ten ?
A Fano threefold of genus ten is a linear section of a fivefold which is homogeneous under the exceptional complex Lie group G_2.
The threefold X determines a rank-three vector bundle E over a smooth curve Y of genus two.
I will speak about work in progress towards the description of the moduli space of Fano threefolds X of genus ten via the Coble cubic of dimension seven associated to Y and the bundle E over Y.
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Gianluca Pacienza (Strasbourg) - Coisotropic subvarieties of holomorphic symplectic varieties
Claire Voisin recently suggested a new approach to study the Chow group
of 0-cycles on holomorphic symplectic varieties. A key rôle in her approach is played by coisotropic subvarieties. In the talk I will present results on the existence of such subvarieties, obtained in a series of papers joint with F. Charles, Ch. Lehn and G. Mongardi.
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Participants
Giuseppe Ancona (Zürich)
Rémi Bignalet-Cazalet (Dijon)
Jérémy Blanc (Basel)
Jung-Kyu Canci (Basel)
Adrien Dubouloz (Dijon)
Daniele Faenzi (Dijon)
Andrea Fanelli (Basel)
Jean-Philippe Furter (Basel)
Mattias Hemmig (Basel)
Hanspeter Kraft (Basel)
Lucy Moser-Jauslin (Dijon)
Gianluca Pacienza (Strasbourg)
Ronan Terpereau (Bonn)
Susanna Zimmermann (Basel)
Send an email to Jeremy  Blanc  unibas ch if you would like to participate.
Organisers
Adrien Dubouloz (Dijon)
Jérémy Blanc (Basel)
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