Symplectic geometry of rationally connected threefolds

Abstract

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.

25 pages. Preliminary version. Comments are welcome

References in corpus (3)

• Birational cobordism invariance of uniruled symplectic manifolds
• Virtual neighborhoods and pseudo-holomorphic curves
• Rationally connected $3$-folds and symplectic geometry

Cited by in corpus (2)

• Orbifold Gromov--Witten theory of weighted blowups
• Fundamental groups of rationally connected symplectic manifolds