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In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930).[-]

In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and ...[+]

14J50 ; 14J28 ; 14J35 ; 14J70 ; 14M15 ; 14N20

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In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930).[-]

In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and ...[+]

14J50 ; 14J28 ; 14J35 ; 14J70 ; 14M15 ; 14N20

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In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and describe some explicit examples. I will give particular attention to double EPW sextics, that admit in a natural way a non-symplectic involution. Time permitting I will show how the rich geometry of double EPW sextics has an important connection to a classical question of U. Morin (1930).[-]

In the 80's Beauville generalized several foundational results of Nikulin on automorphism groups of K3 surfaces to hyperkähler manifolds. Since then the study of automorphism groups of hyperkähler manifolds and in particular of hyperkähler fourfolds got very much attention. I will present some classification results for automorphisms on hyperkähler fourfolds that are deformation equivalent to the Hilbert scheme of two points on a K3 surface and ...[+]

14J50 ; 14J28 ; 14J35 ; 14J70 ; 14M15 ; 14N20

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Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially recovering a result of Laza.[-]

Hyperkähler manifolds are higher-dimensional analogs of K3 surfaces. Verbitsky and Markmann recently proved that their period map is an open embedding. In a joint work with E. Macri, we explicitly determine the image of this map in some cases. I will explain this result together with a nice application (found by Bayer and Mongardi) to the (almost complete) determination of the image of the period map for cubic fourfolds, hereby partially ...[+]

14C34 ; 14E07 ; 14J50 ; 14J60

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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:

* ...[+]

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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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:

* ...[+]

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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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:

* ...[+]

14J10 ; 14J28 ; 14J50 ; 14C20 ; 14C22 ; 14J27 ; 14L30

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We show, among other things, one way to construct a smooth complex projective rational variety of any dimension n ≥ 3, with discrete non-finitely generated automorphism group and with infinitely many mutually non-isomorphic real forms. This is a joint work in progress with Professors Tien-Cuong Dinh and Xun Yu.

14J50

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The automorphism group of a compact Kähler manifold satisfies Tits alternative: any subgroup either admits a solvable subgroup of finite index or contains a free non-abelian group of two generators (Campana-WangZhang). In the first case, this group cannot be too big. Some algebraic (rational) manifolds with special automorphisms admit infinitely many nonequivalent real forms. This talk is based on my (old and recent) works with F. Hu, H.-Y. Lin, V.-A. Nguyen, K. Oguiso, N. Sibony, X. Yu, D.-Q. Zhang.[-]

The automorphism group of a compact Kähler manifold satisfies Tits alternative: any subgroup either admits a solvable subgroup of finite index or contains a free non-abelian group of two generators (Campana-WangZhang). In the first case, this group cannot be too big. Some algebraic (rational) manifolds with special automorphisms admit infinitely many nonequivalent real forms. This talk is based on my (old and recent) works with F. Hu, H.-Y. Lin, ...[+]

14J50 ; 32M05 ; 32H50 ; 37B40

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Great achievements have been made towards the study of realstructures on K3 surfaces. I will report on an attempt to generalize some of these results to higher dimensional analogs of K3 surfaces, namely, the so-called compact hyper-Kähler manifolds. The emphasis will be on finiteness properties of their (Klein) automorphism groups. In particular, we show that there are only finitely many real structures on a given compact hyper-Kähler manifold. It is based on a joint work with Andrea Cattaneo.[-]

Great achievements have been made towards the study of realstructures on K3 surfaces. I will report on an attempt to generalize some of these results to higher dimensional analogs of K3 surfaces, namely, the so-called compact hyper-Kähler manifolds. The emphasis will be on finiteness properties of their (Klein) automorphism groups. In particular, we show that there are only finitely many real structures on a given compact hyper-Kähler manifold. ...[+]

14P99 ; 14J50 ; 53C26

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Documents 14J50 13 résultats

Automorphisms of hyperkähler manifolds​ - Lecture 1 - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Automorphisms of hyperkähler manifolds​ - Lecture 2 - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Automorphisms of hyperkähler manifolds​ - Lecture 3 - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Periods of polarized hyperkähler manifolds​ - Debarre, Olivier (Auteur de la Conférence) | CIRM H Nouveau

Topics on $K3$ surfaces - Lecture 1: $K3$ surfaces in the Enriques Kodaira classification and examples - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

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

Topics on $K3$ surfaces - Lecture 5: Finite automorphism groups - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Projective rational manifolds with non-finitely generated discrete automorphism group and infinitely many real forms - Oguiso, Keiji (Auteur de la Conférence) | CIRM H Nouveau

On the automorphisms of compact Kähler manifolds - Dinh, Tien-Cuong (Auteur de la Conférence) | CIRM H Nouveau

Real structures on hyper-Kähler manifolds - Fu, Lie (Auteur de la Conférence) | CIRM H Nouveau

Automorphisms of hyperkähler manifolds - Lecture 1 - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Automorphisms of hyperkähler manifolds - Lecture 2 - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Automorphisms of hyperkähler manifolds - Lecture 3 - Sarti, Alessandra (Auteur de la Conférence) | CIRM H Nouveau

Periods of polarized hyperkähler manifolds - Debarre, Olivier (Auteur de la Conférence) | CIRM H Nouveau