Demonstrates the finiteness of log surfaces with klt singularities, suggesting new bounds in algebraic geometry.
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 (2026) studied this question.
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