Minimal compactifications of the affine plane with only star-shaped singularities

TL;DR

This paper classifies minimal compactifications of the complex affine plane that have only star-shaped singularities, focusing on those with at most log canonical singularities.

Contribution

It provides a complete classification of minimal compactifications with star-shaped singular points, extending previous classifications to this specific singularity type.

Findings

All minimal compactifications with at most log canonical singularities have only star-shaped singularities.

The classification of such compactifications is achieved.

The results clarify the structure of singularities in minimal compactifications.

Abstract

We consider minimal compactifications of the complex affine plane. Minimal compactifications of the affine plane with at most log canonical singularities are classified. Moreover, every minimal compactification of the affine plane with at most log canonical singularities has only star-shaped singular points. In this article, we classify minimal compactifications of the affine plane with only star-shaped singular points.