Volumes of foliations birationally bounded by algebraically integrable families (2512.21932v1)

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.