A note on $\mathbb{Q}$-Gorenstein surfaces
Abstract
We construct a normal projective $\mathbb{Q}$-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 $\mathbb{Q}$-Gorenstein surfaces, which was previously unknown in positive characteristic.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Geometry and complex manifolds
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 31 January 2026
- Document type
- Preprint