Symplectic geometry of rationally connected threefolds

Details Symplectic geometry of rationally connected threefolds Symplectic geometry of rationally connected threefolds

2010-06-12

arxiv.org/abs/1006.2486v1

Mathematics

Algebraic Geometry

25 pages. Preliminary version. Comments are welcome

Scientific paper

We study symplectic geometry of rationally connected $3$-folds. The first result shows that rationally connectedness is a symplectic deformation invariant in dimension $3$. If a rationally connected $3$-fold $X$ is Fano or $b_2(X)=2$, we prove that it is symplectic rationally connected, i.e. there is a non-zero Gromov-Witten invariant with two insertions being the class of a point. Finally we prove that many rationally connected $3$-folds are birational to a symplectic rationally connected variety.

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