English
On the existence of algebraic approximations of compact Kähler manifolds
Post-edited
Auteurs : Lin, Hsueh-Yung (Auteur de la Conférence)
CIRM (Editeur )
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
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 : Keywords : Kähler manifold; Kodaira problem; Kähler threefold; deformation; fibration
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
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Informations sur la Vidéo
Réalisateur : Recanzone, LucaLangue : Anglais Date de publication : 09/01/2019 Date de captation : 17/12/2018 Sous collection : Research talks arXiv category : Algebraic Geometry ; Complex Variables Domaine : Algebraic & Complex Geometry ; Analysis and its Applications Format : MP4 (.mp4) - HD Durée : 00:50:27 Audience : Researchers Download : https://videos.cirm-math.fr/2018-12-17_Lin.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexeOrganisateurs 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
Données de citation
DOI : 10.24350/CIRM.V.19484103Citer cette vidéo: 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
- [Multi angle] Examples of Kähler groups / Auteur de la Conférence Eyssidieux, Philippe.
- [Multi angle] Algebraic models of the line in the real affine plane / Auteur de la Conférence Mangolte, Frédéric.
- [Multi angle] Random section of line bundles over real Riemann surfaces / Auteur de la Conférence Ancona, Michele.
- [Multi angle] Fano fibrations in positive characteristic / Auteur de la Conférence Fanelli, Andrea.
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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