Cylinders in Du Val del Pezzo surfaces of degree one with Picard rank two

TL;DR

This paper establishes a link between the existence of anticanonical polar cylinders and ample polar cylindricity in Du Val del Pezzo surfaces of degree one with Picard rank two, advancing understanding of their geometric structures.

Contribution

It proves that for these surfaces, the presence of an anticanonical polar cylinder guarantees ample polar cylindricity, a new insight into their geometric properties.

Findings

Anticanonical polar cylinders imply ample polar cylindricity.

Results apply specifically to degree one Du Val del Pezzo surfaces with Picard rank two.

Enhances understanding of the structure of these algebraic surfaces.

Abstract

We prove that for Du Val del Pezzo surfaces of degree one with Picard rank two, the existence of an anticanonical polar cylinder implies the ample polar cylindricity.