Rationally connected $3$-folds and symplectic geometry

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 $b_2(X)\le 2$.

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

References in corpus (1)

• Birational cobordism invariance of uniruled symplectic manifolds

Cited by in corpus (7)

• Symplectic geometry of rationally connected threefolds
• Orbifold Gromov--Witten theory of weighted blowups
• On the symplectic invariance of log Kodaira dimension
• Symplectic geometry and rationally connected 4-folds
• Positive divisors in symplectic geometry
• Weighted blowup correspondence of orbifold Gromov--Witten invariants and applications
• Some examples of symplectic rationally connected 4-folds