A rigid, not infinitesimally rigid surface with K ample

TL;DR

This paper constructs a specific example of a smooth compact complex surface that is rigid but not infinitesimally rigid, with an ample canonical bundle, using line arrangements inspired by notable mathematicians.

Contribution

It provides the first known example of such a surface, expanding understanding of rigidity properties in complex geometry.

Findings

Constructed a rigid, not infinitesimally rigid surface

Used line arrangements inspired by Hirzebruch, Kapovich, Millson, Manetti, Vakil

Demonstrated the existence of surfaces with ample canonical bundle exhibiting this property

Abstract

We produce an example of a rigid, but not infinitesimally rigid smooth compact complex surface with ample canonical bundle using results about arrangements of lines inspired by work of Hirzebruch, Kapovich and Millson, Manetti and Vakil.