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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. 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) = ...

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Documents 32J25 | enregistrements trouvés : 21

On the existence of algebraic approximations of compact Kähler manifolds Lin, Hsueh-Yung | CIRM H Nouveau

Hodge theory :proceedings of the U.S. - spain workshop held in sant cugat barcelona#June 24-30 Cattani, E. ; Guillen, F. ; Kaplan, A. ; Puerta, F. | Springer-Verlag 1987 Nouveau

Algebraic cycles and Hodge theorylectures given at the 2nd session of the centro internazionale matematico estivo (C.I.M.E.) held in June 21-29 Murre, J. ; Voisin , C. ; Albano, A. ; Bardelli, F. | Springer-Verlag 1994 Nouveau

Actes du colloque de théorie de Hodge :Luminy#Juin 1 - 6 | Société Mathématique de France 1989 Nouveau

Séminaire Bourbaki. Vol. 1997/98 :exposés 835-849 | Société Mathématique de France 1998 Nouveau

Higher dimensional complex geometry :a summer seminar at the University of Utah#July - Aug. Clemens, C. Herbert ; Kollár, János ; Mori, Shigefumi | Société Mathématique de France 1988 Nouveau

Groupes de Galois arithmétiques et différentiels#Mars 8-13 Bertrand, Daniel ; Dèbes, Pierre | Société Mathématique de France 2006 Nouveau

Arrangements, local systems and singularitiesCIMPA summer schoolIstanbul # june 11-22, 2007 El Zein, Fouad ; Suciu, Alexander I. ; Tosun, Meral ; Uludag, A. Muhammed ; Yuzvinsky, Sergey | Birkhäuser 2010 Nouveau

Hodge theory.Based on lectures delivered at the summer school on Hodge theory and related topicsTrieste # june 14 - july 2, 2010 Cattani, Eduardo ; El Zein, Fouad ; Griffiths, Phillip A. ; Le, Dung Trang | Princeton University Press 2014 Nouveau

Analysis, complex geometry, and mathematical physics: in honor of Duong H. PhongNew York # May 7-11, 2013 Feehan, Paul M. N. ; Song, Jian ; Weinkove, Ben ; Wentworth, Richard A. | American Mathematical Society 2015 Nouveau

Recent advances in Hodge theory: period domains, algebraic cycles, and arithmetic.Proceedings of the summer school and conferenceVancouver # June 10-20, 2013 Kerr, Matt ; Pearlstein, Gregory | Cambridge University Press 2016 Nouveau

Examples of Kähler groups Eyssidieux, Philippe | CIRM H Nouveau

Compact complex surfaces Barth, W. ; Peters, C. ; Van De Ven , A. | Springer-Verlag 1984 Nouveau

Quelques applications analytiques de la théorie des courbes et des surfaces algébriques Picard, M. Emile | Gauthier-Villars et Cie. 1931 Nouveau

Complex abelian varieties and theta functions Kempf, Georges R. | Springer-Verlag 1991 Nouveau

Transformation groups in differential geometry Kobayashi, Shoshichi | Springer-Verlag 1972 Nouveau

Representations of fundamental groups of algebraic varieties Zuo, Kang | Springer 1999 Nouveau

Notes on gauge theory and Hodge theory Ionesei, Gheorghe | Terra Nostra 2001 Nouveau

Selected works of Phillip A. Griffiths with commentary. Part 3 :variations of Hodge structures Griffiths, Phillip A. ; Clemens, C. Herbert ; Morrison, David R. | American Mathematical Society 2003 Nouveau

Hodge theory and complex algebraic geometry II Voisin, Claire ; Schneps, Leila | Cambridge University Press 2007 Nouveau

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Hodge theory :
proceedings of the U.S. - spain workshop held in sant cugat barcelona#June 24-30 Cattani, E. ; Guillen, F. ; Kaplan, A. ; Puerta, F. | Springer-Verlag 1987 Nouveau

Algebraic cycles and Hodge theory
lectures given at the 2nd session of the centro internazionale matematico estivo (C.I.M.E.) held in June 21-29 Murre, J. ; Voisin , C. ; Albano, A. ; Bardelli, F. | Springer-Verlag 1994 Nouveau

Actes du colloque de théorie de Hodge :
Luminy#Juin 1 - 6 | Société Mathématique de France 1989 Nouveau

Séminaire Bourbaki. Vol. 1997/98 :
exposés 835-849 | Société Mathématique de France 1998 Nouveau

Higher dimensional complex geometry :
a summer seminar at the University of Utah#July - Aug. Clemens, C. Herbert ; Kollár, János ; Mori, Shigefumi | Société Mathématique de France 1988 Nouveau

Arrangements, local systems and singularities
CIMPA summer school
Istanbul # june 11-22, 2007 El Zein, Fouad ; Suciu, Alexander I. ; Tosun, Meral ; Uludag, A. Muhammed ; Yuzvinsky, Sergey | Birkhäuser 2010 Nouveau

Hodge theory.
Based on lectures delivered at the summer school on Hodge theory and related topics
Trieste # june 14 - july 2, 2010 Cattani, Eduardo ; El Zein, Fouad ; Griffiths, Phillip A. ; Le, Dung Trang | Princeton University Press 2014 Nouveau

Analysis, complex geometry, and mathematical physics: in honor of Duong H. Phong
New York # May 7-11, 2013 Feehan, Paul M. N. ; Song, Jian ; Weinkove, Ben ; Wentworth, Richard A. | American Mathematical Society 2015 Nouveau

Recent advances in Hodge theory: period domains, algebraic cycles, and arithmetic.
Proceedings of the summer school and conference
Vancouver # June 10-20, 2013 Kerr, Matt ; Pearlstein, Gregory | Cambridge University Press 2016 Nouveau

Selected works of Phillip A. Griffiths with commentary. Part 3 :
variations of Hodge structures Griffiths, Phillip A. ; Clemens, C. Herbert ; Morrison, David R. | American Mathematical Society 2003 Nouveau