Symplectic geometry and rationally connected 4-folds

TL;DR

This paper explores symplectic geometry in relation to rationally connected 4-folds, establishing conditions under which these complex structures are proven to be rationally connected, thus advancing understanding in algebraic and symplectic geometry.

Contribution

It introduces new symplectic geometric methods to prove rational connectedness for certain classes of 4-folds, expanding the known criteria for rational connectivity.

Findings

Rationally connected 4-folds with specific properties are proven to be rationally connected.

Symplectic deformation invariance of rational connectedness is established for certain 4-folds.

Conditions involving pseudo-index and Betti number influence rational connectedness.

Abstract

We study some symplectic geometric aspects of rationally connected 4-folds. As a corollary, we prove that any smooth projective 4-fold symplectic deformation equivalent to a Fano 4-fold of pseudo-index at least 2 or a rationally connected 4-fold whose second Betti number is 2 is rationally connected.