K*-surfaces of Picard number one and integral degree

TL;DR

This paper classifies certain algebraic surfaces with specific geometric properties, providing explicit descriptions of those with Picard number one, torus actions, and integral canonical self-intersection.

Contribution

It offers a complete explicit classification of quasismooth rational surfaces with Picard number one under specified conditions.

Findings

Explicit descriptions of all such surfaces.

Identification of surfaces with integral canonical self-intersection.

Characterization of surfaces admitting torus actions.

Abstract

We give an explicit description of all quasismooth, rational, projective surfaces of Picard number one that admit a non-trivial torus action and have an integral canonical self intersection number.