On volumes and the generic invariance of Fano type varieties

2025/06/16 by Donghyeon Kim, Kim, Donghyeon · 1 citation
Mathematics · #14E05 #14E30 #14G17 #14J45 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2506.13603

openalex publication_date 2025/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension 2. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod p.

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• Asymptotically flat divisors and strongly F-regular type varieties

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