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arXiv · 2512.21932

Volumes of foliations birationally bounded by algebraically integrable families

Zhixiu Fan
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Abstract

We prove that for log canonical foliations which are birationally bounded by algebraically integrable families, the set of their volumes satisfies the DCC. This answers a special case of a question posed by Cascini, Hacon, and Langer. As a key ingredient, we establish the deformation invariance of relative log canonical volumes for a family of weak semistable morphisms, which can be viewed as a relative version of the classical result proved by Hacon, McKernan, and Xu.

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Zhixiu Fan. 2025-12-26. Volumes of foliations birationally bounded by algebraically integrable families. https://arxiv.org/abs/2512.21932

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