Rationally connected $3$-folds and symplectic geometry

Claire Voisin

Rationally connected $3$-folds and symplectic geometry

Algebraic Geometry 2008-03-27 v5 Symplectic Geometry

Authors: 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 $X$ is Fano or $b_2(X)\leq2$ .

Keywords

fano varieties manifolds

Cite

@article{arxiv.0801.1396,
  title  = {Rationally connected $3$-folds and symplectic geometry},
  author = {Claire Voisin},
  journal= {arXiv preprint arXiv:0801.1396},
  year   = {2008}
}

Comments

New 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

Related papers

View all related →