Remarks on Donaldson's symplectic submanifolds

TL;DR

This paper discusses the topology and geometry of symplectic hyperplane sections, proving that their complements are Weinstein and Stein manifolds for large degrees, which advances understanding of symplectic topology.

Contribution

It provides a detailed proof that complements of Donaldson's symplectic hyperplane sections are Weinstein and Stein manifolds at high degrees, clarifying their geometric structure.

Findings

Complements of Donaldson's symplectic hyperplane sections are Weinstein manifolds.

These complements are also Stein manifolds, though less naturally.

The results hold for sufficiently large degrees.

Abstract

This paper presents a few remarks about the topology of symplectic hyperplane sections and the geometry of their complements. In particular, it contains a detailed proof of the following result already stated with hints in [Gi]: for sufficiently large degrees, the complements of Donaldson's symplectic hyperplane sections are naturally Weinstein --- and less naturally Stein --- manifolds.