Genus Zero One Point Correlators of Subcritical Stein Manifolds

TL;DR

This paper computes specific genus zero one-point correlators for subcritical Stein fillings with vanishing first Chern class, advancing the understanding of their potential functions and implications for uniruledness of certain Kähler manifolds.

Contribution

It determines the genus zero one-point correlators for a class of subcritical Stein manifolds, linking symplectic invariants to algebraic geometric properties.

Findings

Computed genus zero one-point correlators for subcritical Stein fillings

Established conditions under which a Kähler manifold is uniruled

Connected symplectic invariants to algebraic geometric properties

Abstract

We determine the one point genus zero correlators of compactly supported forms of a subcritical Stein filling whose first Chern class vanishes. This is a step towards determining the full potential function of the filling. As an application, we proved that if a K\"{a}hler manifold $M^{2n}$ admits a subcritical polarization and $c_1$ vanishes in the subcritical complement, then $M$ is uniruled.