Contractibility of the geometric stability manifold of a surface

TL;DR

This paper proves that the geometric stability manifold of any smooth projective complex surface is contractible and identifies new families of surfaces with this property.

Contribution

It establishes the contractibility of the geometric stability manifold for all smooth projective complex surfaces and finds infinitely many new such families.

Findings

Geometric stability manifold of any smooth projective complex surface is contractible.

Identifies infinitely many new families of surfaces with contractible stability manifolds.

Abstract

Using a recent description of the geometric stability manifold, we show the geometric stability manifold associated to any smooth projective complex surface is contractible. We then use this result to demonstrate infinitely many new families of surfaces whose stability manifold is contractible.