Rational ruled surfaces as symplectic hyperplane sections

TL;DR

This paper investigates the conditions under which rational ruled surfaces can be embedded as symplectic hyperplane sections in closed symplectic manifolds, with implications for Stein fillability of certain bundles.

Contribution

It provides new criteria for embedding rational ruled surfaces as symplectic hyperplane sections and explores their impact on Stein fillability of Boothby–Wang bundles.

Findings

Criteria for embedding rational ruled surfaces as symplectic hyperplane sections

Results on Stein fillability of Boothby–Wang bundles over these surfaces

Connections between symplectic embeddings and bundle fillability

Abstract

We study embeddability of rational ruled surfaces as symplectic hyperplane sections into closed integral symplectic manifolds. From this we obtain results on Stein fillability of Boothby--Wang bundles over rational ruled surfaces.