Rationally connected $3$-folds and symplectic geometry

Details Rationally connected $3$-folds and symplectic geometry Rationally connected $3$-folds and symplectic geometry

2008-01-09

arxiv.org/abs/0801.1396v5

Mathematics

Algebraic Geometry

New final version. The statement is improved, thanks to the help of Jason Starr. Indeed, the result holds now for general sypl

Scientific paper

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 $b_2(X)\leq2$.

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