Asymptotic base loci on hyper-Kähler manifolds

2023/04/04 by Francesco Antonio Denisi, Denisi, Francesco Antonio, Ángel David Ríos Ortiz +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2304.01773

openalex publication_date 2023/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a projective hyper-Kähler manifold X, we study the asymptotic base loci of big divisors on X. We provide a numerical characterization of these loci and study how they vary while moving a big divisor class in the big cone, using the divisorial Zariski decomposition, and the Beauville-Bogomolov-Fujiki form. We determine the dual of the cones of k-ample divisors Amp_k(X), for any 1≤ k ≤ dim(X), answering affirmatively (in the case of projective hyper-Kähler manifolds) a question asked by Sam Payne. We provide a decomposition for the effective cone Eff(X) into chambers of Mori-type, analogous to that for Mori dream spaces into Mori chambers. To conclude, we illustrate our results with several examples.

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