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Locally stable degenerations of log Calabi-Yau pairs

Published 16 Feb 2023 in math.AG | (2302.08352v1)

Abstract: We study the birational boundedness of special fibers of log Calabi-Yau fibrations and Fano fibrations. We show that for a locally stable family of Fano varieties or polarised log Calabi-Yau pairs over a curve, if the general fiber satisfies some natural boundedness conditions, then every irreducible component of the special fiber is birationally bounded.

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