0801.1396Jan 9, 2008New final version. The statement is improved, thanks to the help of Jason Starr. Indeed, the result holds now for general syplectic equivalence, and not the restricted notion of symplectic equivalence we used before
Rationally connected 3-folds and symplectic geometry
Claire Voisin
Abstract
We study the following question, asked to us By Pandharipande and Starr: Let X be a rationally connected 3-fold, and Y be a compact Kaehler 3-fold symplectically equivalent to it. Is Y rationally connected? We show that the answer is positive if X