Positive divisors in symplectic geometry

TL;DR

This paper explores the relationship between absolute and relative Gromov-Witten invariants in symplectic geometry and establishes conditions under which a symplectic manifold is rationally connected based on the presence of a positive divisor.

Contribution

It provides explicit relations between Gromov-Witten invariants and characterizes symplectic rational connectivity via positive divisors.

Findings

Established explicit relations between absolute and relative Gromov-Witten invariants.

Proved that containing a positive divisor symplectomorphic to projective space implies rational connectivity.

Connected the existence of certain divisors to symplectic rational connectivity.

Abstract

In this paper, we gave some explicit relations between absolute and relative Gromov-Witten invariants. We proved that a symplectic manifold is symplectic rationally connected if it contains a positive divisor symplectomorphic to $P^n$.