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H 1 On the existence of algebraic approximations of compact Kähler manifolds

Auteurs : Lin, Hsueh-Yung (Auteur de la Conférence)
CIRM (Editeur )

 Loading the player... Kodaira problem compact Kähler threefolds fibrations in abelian varieties isotrivial fibrations in K-trivial surfaces uniruled threefolds

Résumé : Let $X$ be a compact Kähler manifold. The so-called Kodaira problem asks whether $X$ has arbitrarily small deformations to some projective varieties. While Kodaira proved that such deformations always exist for surfaces. Starting from dimension 4, there are examples constructed by Voisin which answer the Kodaira problem in the negative. In this talk, we will focus on threefolds, as well as compact Kähler manifolds of algebraic dimension $a(X) = dim(X) -1$. We will explain our positive solution to the Kodaira problem for these manifolds.

Keywords : Kähler manifold; Kodaira problem; Kähler threefold; deformation; fibration

Codes MSC :
14D06 - Fibrations, degenerations
14E30 - Minimal model program (Mori theory, extremal rays)
32G05 - Deformations of complex structures
32J17 - Compact $3$-folds (analytic spaces)
32J25 - Transcendental methods of algebraic geometry
32J27 - Compact Kähler manifolds: generalizations, classification

 Informations sur la Vidéo Réalisateur : Recanzone, Luca Langue : Anglais Date de publication : 09/01/2019 Date de captation : 17/12/2018 Collection : Research talks Format : MP4 (.mp4) - HD Durée : 00:50:27 Domaine : Algebraic & Complex Geometry ; Analysis and its Applications Audience : Chercheurs ; Doctorants , Post - Doctorants Download : https://videos.cirm-math.fr/2018-12-17_Lin.mp4 Informations sur la rencontre Nom de la rencontre : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexeOrganisateurs de la rencontre : Benoist, Olivier ; Pasquier, BorisDates : 17/12/2018 - 21/12/2018 Année de la rencontre : 2018 URL Congrès : https://conferences.cirm-math.fr/1858.html Citation Data DOI : 10.24350/CIRM.V.19484103 Cite this video as: Lin, Hsueh-Yung (2018). On the existence of algebraic approximations of compact Kähler manifolds. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19484103 URI : http://dx.doi.org/10.24350/CIRM.V.19484103

### Voir aussi

Bibliographie

• Lin, H-Y. (2017). Algebraic approximations of compact Kähler threefolds of Kodaira dimension 0 or 1.〈arXiv:1704.08109〉 - https://arxiv.org/abs/1704.08109

• Lin, H-Y. (2018). Algebraic approximations of uniruled compact Kähler threefolds.〈arXiv:1710.01083〉 - https://arxiv.org/abs/1710.01083

• Lin, H-Y. Algebraic approximations of compact Kähler manifolds of algebraic codimension 1, to appear -

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