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The algebraic delta invariant, a number encoding the K-stability of a Fano variety, is a central theme of this Winter school. In the first lecture, T. Delcroix presents an analytic viewpoint on the delta invariant developped by Kewei Zhang, along with the rough ideas of the variational approach to existence of canonical Kähler metrics. In his second lecture, he extends this to the weighted Kähler setting (joint work with S. Jubert), allowing to deal with Kähler-Ricci solitons and more. [-]

The algebraic delta invariant, a number encoding the K-stability of a Fano variety, is a central theme of this Winter school. In the first lecture, T. Delcroix presents an analytic viewpoint on the delta invariant developped by Kewei Zhang, along with the rough ideas of the variational approach to existence of canonical Kähler metrics. In his second lecture, he extends this to the weighted Kähler setting (joint work with S. Jubert), allowing to ...[+]

32Q20 ; 53C55 ; 53C25

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The algebraic delta invariant, a number encoding the K-stability of a Fano variety, is a central theme of this Winter school. In the first lecture, T. Delcroix presents an analytic viewpoint on the delta invariant developped by Kewei Zhang, along with the rough ideas of the variational approach to existence of canonical Kähler metrics. In his second lecture, he extends this to the weighted Kähler setting (joint work with S. Jubert), allowing to deal with Kähler-Ricci solitons and more. [-]

The algebraic delta invariant, a number encoding the K-stability of a Fano variety, is a central theme of this Winter school. In the first lecture, T. Delcroix presents an analytic viewpoint on the delta invariant developped by Kewei Zhang, along with the rough ideas of the variational approach to existence of canonical Kähler metrics. In his second lecture, he extends this to the weighted Kähler setting (joint work with S. Jubert), allowing to ...[+]

32Q20 ; 53C55 ; 53C25

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I will introduce the concept of K-moduli illustrated by some examples of moduli spaces and related comparisons with GIT and wall-crossing phenomenon.

14J10

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I will introduce the concept of K-moduli illustrated by some examples of moduli spaces and related comparisons with GIT and wall-crossing phenomenon.

14J10

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Let f : X → Y be a holomorphic map between compact Kähler manifolds. If a general fibre of f is a projective manifold a natural question is whether the morphism itself is projective, i.e. X embeds into some projectivised bundle P(V) → Y. It is well-known that this is not the case, but we will see that in some situations that are natural in the context of MMP, the answer is yes.

32J25 ; 32Q15 ; 14E30

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We will start with a brief introduction to topology of real algebraic curves, and then will discuss in more details the case of curves of degree 6 in the real projective plane. We will show that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, that is, the polarization, exceptional divisors, and real structure recorded in the homology of the covering K3-surface. We will also present an Arnold-Gudkov-Rokhlin type congruence for real algebraic curves/surfaces with certain singularities.[-]

We will start with a brief introduction to topology of real algebraic curves, and then will discuss in more details the case of curves of degree 6 in the real projective plane. We will show that the equisingular deformation type of a simple real plane sextic curve with smooth real part is determined by its real homological type, that is, the polarization, exceptional divisors, and real structure recorded in the homology of the covering ...[+]

14J28 ; 14P25 ; 14H50

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An algebraic variety is said to be rational if it is birational to projective space. In this talk, westudy the rationality question over the real numbers for a certain class of conic bundle threefolds.The varieties we consider all become rational over the complex numbers, but in general the complex rationality construction need not descend to $ \mathbb{R}$. We discuss rationality obstructions coming from intermediate Jacobian torsors and from the real loci of these varieties.[-]

An algebraic variety is said to be rational if it is birational to projective space. In this talk, westudy the rationality question over the real numbers for a certain class of conic bundle threefolds.The varieties we consider all become rational over the complex numbers, but in general the complex rationality construction need not descend to $ \mathbb{R}$. We discuss rationality obstructions coming from intermediate Jacobian torsors and from ...[+]

14E08 ; 14C25 ; 14P99

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This talk will discuss some examples of K-moduli spaces of Fano 3-folds and their relationship to other modular constructions.

14J45 ; 14E07 ; 14D22

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Many nice Fano manifolds and K3 surfaces can be obtained as linear sections of homogeneous spaces. I will study low-codimensional sections of the spinor tenfold, that admit non-trivial moduli starting from codimension four. The corresponding family exhibits an extremely rich geometry, connected with the exceptional complex Lie algebra of type E 8, the theory of graded Lie algebras, as well as the classical Kummer quartic surfaces in three dimensional projective space.[-]

Many nice Fano manifolds and K3 surfaces can be obtained as linear sections of homogeneous spaces. I will study low-codimensional sections of the spinor tenfold, that admit non-trivial moduli starting from codimension four. The corresponding family exhibits an extremely rich geometry, connected with the exceptional complex Lie algebra of type E 8, the theory of graded Lie algebras, as well as the classical Kummer quartic surfaces in three ...[+]

14J30 ; 14J45 ; 14J60

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Documents Cheltsov, Ivan 9 résultats

Analytic delta invariant and weighted Kähler geometry Lecture 1 - Delcroix, Thibaut (Auteur de la conférence) | CIRM H Nouveau

Analytic delta invariant and weighted Kähler geometry Lecture 2 - Delcroix, Thibaut (Auteur de la conférence) | CIRM H Nouveau

Introduction to K-moduli Lecture 1 - Devleming, Kristin (Auteur de la conférence) | CIRM H Nouveau

Introduction to K-moduli Lecture 2 - Devleming, Kristin (Auteur de la conférence) | CIRM H Nouveau

Projectivity criteria for Kähler morphisms - Höring, Andreas (Auteur de la conférence) | CIRM H Nouveau

Real plane sextic curves without real singular points - Itenberg, Ilia (Auteur de la conférence) | CIRM H Nouveau

Rationality of some real conic bundle threefolds - Ji, Lena (Auteur de la conférence) | CIRM H Nouveau

Explicit K-moduli spaces of Fano 3-folds - Kaloghiros, Anne-Sophie (Auteur de la conférence) | CIRM H Nouveau

A family of Fano manifolds obtained as linear sections of the spinor tenfold - Manivel, Laurent (Auteur de la conférence) | CIRM H Nouveau