Variation of cones of divisors in a family of varieties -- Fano type case

2025/04/05 by Sung Rak Choi, Zhan Li, Choi, Sung Rak +3 · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2504.04109

openalex publication_date 2025/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the relationship between the Fano type property on fibers over a Zariski dense subset and the global Fano type property. We establish the invariance of Néron-Severi spaces, nef cones, effective cones, movable cones, and Mori chamber decompositions for a family of Fano type varieties after a generically finite base change. Additionally, we show the uniform behavior of the minimal model program for this family. These results are applied to the boundedness problem of Fano type varieties.

Cited by

• Asymptotically flat divisors and strongly F-regular type varieties
• Finiteness of K-moduli compactifications

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