On the geography of symplectic 4-manifolds with divisible canonical class

TL;DR

This paper explores the classification of simply-connected symplectic 4-manifolds considering the divisibility of their canonical class, and presents new examples with multiple inequivalent symplectic structures.

Contribution

It introduces a refined geography question incorporating canonical class divisibility and provides new examples of 4-manifolds with multiple inequivalent symplectic structures.

Findings

New examples of symplectic 4-manifolds with multiple structures

Refined classification considering canonical class divisibility

Insights into symplectic structure inequivalence

Abstract

In this article we consider a version of the geography question for simply-connected symplectic 4-manifolds that takes into account the divisibility of the canonical class as an additional parameter. We also find new examples of 4-manifolds admitting several symplectic structures, inequivalent under deformation and self-diffeomorphisms of the manifold.