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On the existence of algebraic approximations of compact Kähler manifolds

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Post-edited
Authors : Lin, Hsueh-Yung (Author of the conference)
CIRM (Publisher )

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Kodaira problem compact Kähler threefolds fibrations in abelian varieties isotrivial fibrations in K-trivial surfaces uniruled threefolds
Abstract : 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

MSC Codes :
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
    Information on the Video

    Language : English
    Available date : 09/01/2019
    Conference Date : 17/12/2018
    Subseries : Research talks
    arXiv category : Algebraic Geometry ; Complex Variables
    Mathematical Area(s) : Algebraic & Complex Geometry ; Analysis and its Applications
    Format : MP4 (.mp4) - HD
    Video Time : 00:50:27
    Targeted Audience : Researchers
    Download : https://videos.cirm-math.fr/2018-12-17_Lin.mp4
Information on the Event

Event Title : Algebraic geometry and complex geometry / Géométrie algébrique et géométrie complexe
Event Organizers : Benoist, Olivier ; Pasquier, Boris
Dates : 17/12/2018 - 21/12/2018
Event Year : 2018
Event URL : 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

Bibliography

  • 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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