English

A Note on $\mathbb{Q}$-Gorenstein surfaces

Algebraic Geometry 2026-02-03 v1

Abstract

We construct a normal projective Q\mathbb{Q}-Gorenstein surface over an algebraically closed field whose canonical ring is not finitely generated. Moreover, we provide a counterexample to the minimal model program for Q\mathbb{Q}-Gorenstein surfaces, which was previously unknown in positive characteristic.

Keywords

Cite

@article{arxiv.2602.00732,
  title  = {A Note on $\mathbb{Q}$-Gorenstein surfaces},
  author = {Nao Moriyama},
  journal= {arXiv preprint arXiv:2602.00732},
  year   = {2026}
}

Comments

14 pages

R2 v1 2026-07-01T09:29:27.581Z