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# Videothèque  | enregistrements trouvés : 50

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## Multi angle  Topics on $K3$ surfaces - Lecture 2: Kummer surfaces Sarti, Alessandra (Auteur de la Conférence) | CIRM (Editeur )

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

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## Multi angle  Topics on $K3$ surfaces - Lecture 4: Nèron-Severi group and automorphisms Sarti, Alessandra (Auteur de la Conférence) | CIRM (Editeur )

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

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## Multi angle  Topics on $K3$ surfaces - Lecture 6: Classification Sarti, Alessandra (Auteur de la Conférence) | CIRM (Editeur )

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

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## Multi angle  Topics on $K3$ surfaces - Lecture 3: Basic properties of $K3$ surfaces Sarti, Alessandra (Auteur de la Conférence) | CIRM (Editeur )

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

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## Multi angle  Topics on $K3$ surfaces - Lecture 5: Finite automorphism groups Sarti, Alessandra (Auteur de la Conférence) | CIRM (Editeur )

Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* $K3$ surfaces in the Enriques-Kodaira classification.
* Examples; Kummer surfaces.
* Basic properties of $K3$ surfaces; Torelli theorem and surjectivity of the period map.
* The study of automorphisms on $K3$ surfaces: basic facts, examples.
* Symplectic automorphisms of $K3$ surfaces, classification, moduli spaces.
Aim of the lecture is to give an introduction to $K3$ surfaces, that are special algebraic surfaces with an extremely rich geometry. The most easy example of such a surface is the Fermat quartic in complex three-dimensional space.
The name $K3$ was given by André Weil in 1958 in honour of the three remarkable mathematicians: Kummer, Kähler and Kodaira and of the beautiful K2 mountain at Cachemire.
The topics of the lecture are the following:

* ...

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## Multi angle  Moduli of algebraic varieties Dervan, Ruadhai (Auteur de la Conférence) | CIRM (Editeur )

One of the central problems in algebraic geometry is to form a reasonable (e.g. Hausdorff) moduli space of smooth polarised varieties. I will show how one can solve this problem using canonical Kähler metrics. This is joint work with Philipp Naumann.

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## Multi angle  Apriori estimates for scalar curvature type equations on compact Kähler manifolds Cheng, Jingrui (Auteur de la Conférence) | CIRM (Editeur )

We develop apriori estimates for scalar curvature type equations on compact Kähler manifolds. As an application, we show that K-energy being proper with respect to $L^1$ geodesic distance implies the existence of constant scalar curvature Kähler metrics. This is joint work with Xiuxiong Chen.

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## Multi angle  Pluripotential Kähler-Ricci flows Guedj, Vincent (Auteur de la Conférence) | CIRM (Editeur )

We develop a parabolic pluripotential theory on compact Kähler manifolds, defining and studying weak solutions to degenerate parabolic complex Monge-Ampere equations. We provide a parabolic analogue of the celebrated Bedford-Taylor theory and apply it to the study of the Kähler-Ricci flow on varieties with log terminal singularities.

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## Multi angle  Kodaira dimension of algebraic fiber spaces over abelian varieties or projective surfaces Cao, Junyan (Auteur de la Conférence) | CIRM (Editeur )

Let $f : X \to Y$ be a fibration between two projective manifolds. The Iitaka’s conjecture predicts that the Kodaira dimension of $X$ is larger than the sum of the Kodaira dimension of $X$ and the Kodaira dimension of the generic fiber. We explain a proof of the Iitaka conjecture for algebraic fiber spaces over abelian varieties or projective surfaces.
It is a joint work with Mihai Paun.

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## Multi angle  ​Absolute sets and the Decomposition Theorem Budur, Nero (Auteur de la Conférence) | CIRM (Editeur )

We give a new, more conceptual proof of the Decomposition Theorem for semisimple perverse sheaves of rank-one origin, assuming it for those of constant-sheaf origin, that is, assuming the geometric case proven by Beilinson-Bernstein-Deligne-Gabber. Joint work with Botong Wang.

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## Multi angle  Arithmetic of rank one local systems Esnault, Hélène (Auteur de la Conférence) | CIRM (Editeur )

Joint with Moritz Kerz. We study arithmetic subvarieties of the character variety of normal complex varieties defined over a field of finite type.

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## Multi angle  On the B-Semiampleness Conjecture Floris, Enrica (Auteur de la Conférence) | CIRM (Editeur )

An lc-trivial fibration $f : (X, B) \to Y$ is a fibration such that the log-canonical divisor of the pair $(X, B)$ is trivial along the fibres of $f$. As in the case of the canonical bundle formula for elliptic fibrations, the log-canonical divisor can be written as the sum of the pullback of three divisors: the canonical divisor of $Y$; a divisor, called discriminant, which contains informations on the singular fibres; a divisor, called moduli part, that contains informations on the variation in moduli of the fibres. The moduli part is conjectured to be semiample. Ambro proved the conjecture when the base $Y$ is a curve. In this talk we will explain how to prove that the restriction of the moduli part to a hypersurface is semiample assuming the conjecture in lower dimension. This is a joint work with Vladimir Lazić.
An lc-trivial fibration $f : (X, B) \to Y$ is a fibration such that the log-canonical divisor of the pair $(X, B)$ is trivial along the fibres of $f$. As in the case of the canonical bundle formula for elliptic fibrations, the log-canonical divisor can be written as the sum of the pullback of three divisors: the canonical divisor of $Y$; a divisor, called discriminant, which contains informations on the singular fibres; a divisor, called moduli ...

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## Multi angle  Stably irrational hypersurfaces of small slopes Schreieder, Stefan (Auteur de la Conférence) | CIRM (Editeur )

We show that over any uncountable field of characteristic different from two, a very general hypersurface of dimension $n > 2$ and degree at least $log_2 (n) + 2$ is not stably rational. This significantly improves earlier results of Kollár and Totaro. As a byproduct of our proof, we obtain new counterexamples to the integral Hodge conjecture, answering a question of Voisin and Colliot-Thélène - Voisin.

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## Multi angle  A Grassmannian technique and the Kobayashi Conjecture Riedl, Eric (Auteur de la Conférence) | CIRM (Editeur )

An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces $X$ in $\mathbb{P}^n$: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of $X$, and the Kobayashi Conjecture, which says that X contains no entire curves.
We prove that (a slightly strengthened version of) the Green-Griffiths-Lang Conjecture in dimension $2n$ implies the Kobayashi Conjecture in dimension $n$. The technique has already led to improved bounds for the Kobayashi Conjecture. This is joint work with David Yang.
An entire curve on a complex variety is a holomorphic map from the complex numbers to the variety. We discuss two well-known conjectures on entire curves on very general high-degree hypersurfaces $X$ in $\mathbb{P}^n$: the Green-Griffiths-Lang Conjecture, which says that the entire curves lie in a proper subvariety of $X$, and the Kobayashi Conjecture, which says that X contains no entire curves.
We prove that (a slightly strengthened version ...

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## Multi angle  Arithmetic and algebraic hyperbolicity Javanpeykar, Ariyan (Auteur de la Conférence) | CIRM (Editeur )

The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have only finitely many solutions in the integers?”. Namely, if the zeroes of such a system define a hyperbolic variety, then this system should have only finitely many integer solutions.
In this talk I will explain how to verify some of the algebraic, analytic, and arithmetic predictions this conjecture makes. I will present results that are joint work with Ljudmila Kamenova.
The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of “rational points”. For instance, it suggests a striking answer to the fundamental question “Why do some polynomial equations with integer coefficients have only finitely many solutions in the integers?”. Namely, if the zeroes of such a system define a hyperbolic variety, then this system should have only finitely many integer ...

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## Multi angle  ​Special manifolds, the core fibration, rational and entire curves Campana, Frédéric (Auteur de la Conférence) | CIRM (Editeur )

For complex projective manifolds $X$ of general type, Lang claimed the equivalence between three fields: birational geometry, complex hyperbolicity, and arithmetic. We extend this equivalence to arbitrary $X$’s by introducing the (antithetical) class of “Special” manifolds and constructing the “Core” fibration, the unique one with special fibres and general type “orbifold” base. We conjecture that special manifolds —which are defined algebro-geometrically by a certain non-positivity of their cotangent bundles— are also exactly the ones having Zariski-dense entire curves (so violating the GGL property). We shall give (j.w. J. Winkelmann) some examples supporting this conjecture. The arithmetic aspect will be skipped.
For complex projective manifolds $X$ of general type, Lang claimed the equivalence between three fields: birational geometry, complex hyperbolicity, and arithmetic. We extend this equivalence to arbitrary $X$’s by introducing the (antithetical) class of “Special” manifolds and constructing the “Core” fibration, the unique one with special fibres and general type “orbifold” base. We conjecture that special manifolds —which are defined al...

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## Multi angle  ​​​Isotriviality for families given by regular foliations Amerik, Ekaterina (Auteur de la Conférence) | CIRM (Editeur )

Viehweg and Zuo obtained several results concerning the moduli number in smooth families of polarized varieties with semi-ample canonical class over a quasiprojective base. These results led Viehweg to conjecture that the base of a family of maximal variation is of log-general type, and the conjecture has been recently proved by Campana and Paun.
From the “opposite” side, Taji proved that a smooth projective family over a special (in the sense of Campana) quasiprojective base is isotrivial.
We extend Taji’s theorem to quasismooth families, that is, families of leaves of compact foliations without singularities. This is a joint work with F. Campana
Viehweg and Zuo obtained several results concerning the moduli number in smooth families of polarized varieties with semi-ample canonical class over a quasiprojective base. These results led Viehweg to conjecture that the base of a family of maximal variation is of log-general type, and the conjecture has been recently proved by Campana and Paun.
From the “opposite” side, Taji proved that a smooth projective family over a special (in the sense ...

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## Multi angle  ​Construction of lattices defining fake projective planes - Lecture 3 Steger, Tim (Auteur de la Conférence) | CIRM (Editeur )

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## Multi angle  ​Construction of lattices defining fake projective planes - Lecture 4 Cartwright, Donald I. (Auteur de la Conférence) | CIRM (Editeur )

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