Minimal Compactifications of the Affine Plane with only Star-shaped Singularities

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.

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Publication Details

Journal
Taiwanese Journal of Mathematics
Published
2025-03-05
DOI
https://doi.org/10.11650/tjm/250202
Primary Topic
Computational Geometry and Mesh Generation
Type
article
Field-Weighted Citation Impact
0.00

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article

Minimal Compactifications of the Affine Plane with only Star-shaped Singularities

Masatomo Sawahara
Taiwanese Journal of Mathematics
Computational Geometry and Mesh Generation
article

Minimal Compactifications of the Affine Plane with only Star-shaped Singularities

Masatomo Sawahara
article en

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.

Taiwanese Journal of MathematicsVol. 29(3)
Hirosaki University (JP)
Japan Society for the Promotion of Science
Sustainable cities and communities
Openalex Percentile: Top 86%
Computational Geometry and Mesh Generation
DOIOpen Access PDFOpenAlex
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Minimal Compactifications of the Affine Plane with only Star-shaped Singularities — Masatomo Sawahara · Taiwanese Journal of Mathematics (2025) | TGRS Research Map | TGRS