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arXiv · 2510.14795

On the finiteness of log surfaces

Daniil Serebrennikov
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Abstract

We generalize the Kawamata-Matsuki conjecture to klt log pairs and prove it in dimension two. More precisely, we show that a log surface admits only finitely many weakly log canonical projective models with klt singularities up to log isomorphism, by reducing the problem to boundedness of polarizations.

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Daniil Serebrennikov. 2025-10-16. On the finiteness of log surfaces. https://arxiv.org/abs/2510.14795

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