English

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

Algebraic Geometry 2025-05-21 v3

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.

Keywords

Cite

@article{arxiv.2408.07987,
  title  = {Minimal compactifications of the affine plane with only star-shaped singularities},
  author = {Masatomo Sawahara},
  journal= {arXiv preprint arXiv:2408.07987},
  year   = {2025}
}

Comments

16 pages, 4 figures; v3: Corrected many typos. To appear in Taiwanese Journal of Mathematics