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Volume of algebraically integrable foliations and locally stable families
- Publication Year :
- 2024
-
Abstract
- In this paper, we study the volume of algebraically integrable foliations and locally stable families. We show that, for any canonical algebraically integrable foliation, its volume belongs to a discrete set depending only on its rank and the volume of its general leaves. In particular, if the foliation is of general type, then its volume has a positive lower bound depending only on its rank and the volume of its general leaves. This implies some special cases of a question posed by Cascini, Hacon, and Langer. As a consequence, we show that the relative volume of a stable family with a normal generic fiber belongs to a discrete set if the dimension and the volume of its general fibers are bounded. Log versions of the aforementioned theorems are also provided and proved.<br />Comment: 24 pages
- Subjects :
- Mathematics - Algebraic Geometry
Mathematics - Dynamical Systems
14E30, 37F75
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2406.16604
- Document Type :
- Working Paper