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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 )

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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

    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 complexe
Organisateurs de la rencontre : Benoist, Olivier ; Pasquier, Boris
Dates : 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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