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Pré-Publication, Document De Travail Année : 2008

Rationally connected $3$-folds and symplectic geometry

Résumé

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 $b_2(X)\leq2$. We also show that if a conjecture of Ruan on the invariance of Gromov-Witten invariants under blow-ups is true, then the answer is always positive.
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Dates et versions

hal-00203173 , version 1 (09-01-2008)
hal-00203173 , version 2 (11-01-2008)
hal-00203173 , version 3 (02-02-2008)
hal-00203173 , version 4 (21-02-2008)
hal-00203173 , version 5 (27-03-2008)

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Citer

Claire Voisin. Rationally connected $3$-folds and symplectic geometry. 2008. ⟨hal-00203173v1⟩
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