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arXiv · 2602.00732

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

Nao Moriyama
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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.

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Nao Moriyama. 2026-01-31. A note on $\mathbb{Q}$-Gorenstein surfaces. https://arxiv.org/abs/2602.00732

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