Relative augmented base loci on noetherian schemes

2023/06/12 by Yusuke Ushiro, Ushiro, Yusuke
Mathematics · Physics and Astronomy · #14A15 #14E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2306.07127

openalex publication_date 2023/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f:X → S be a projective morphism of noetherian schemes and let L be an invertible sheaf on X. We show that the relative augmented base locus of L coincides with the relative exceptional locus of L. We also prove a semi-ampleness criterion in terms of the exceptional locus generalizing the result of Keel.

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