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Astérisque - Titles - 322 (2008) 1-21

Titles < 2008 < 322

Géométrie différentielle, physique mathématique, mathématiques et société (II)
Volume en l'honneur de Jean Pierre Bourguignon

Oussama Hijazi (éditeur)
Astérisque 322 (2008), xvi+256 pages
Buy the book
Presentation, Summary

Rationally connected 3-folds and symplectic geometry
Claire Voisin
Astérisque 322 (2008), 1-21

Résumé :
3-variétés rationnellement connexes et géométrie symplectique
Nous étudions la question suivante posée par Kollár: soient X et Y des variétés   kählériennes compactes  de dimension 3 symplectiquement équivalentes.  On suppose que X est rationnellement connexe. Y est-elle aussi rationnellement connexe? Nous montrons que la réponse est positive si X est une variété de Fano ou b_2(X)łeq 2.

Mots-clefs : Connectivité rationnelle, Kähler, symplecticité, invariants de Gromov-Witten

Abstract:
We study the following question asked  by Kollár: Let X be a rationally connected 3-fold, and Y be a compact Kähler 3-fold symplectically equivalent to it. Is Y rationally connected? We show that the answer is positive if X is Fano or b_2(X)łeq 2.

Keywords: Rationally connected, Kähler, symplectic, Gromov-Witten invariants

Class. math. : 14M99, 14N35, 14J45, 53D45


ISSN : 0303-1179
Publié avec le concours de : Centre National de la Recherche Scientifique

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