On Hyperkähler manifolds of K3^[n]-type with large Picard number

2024/08/29 by Yulieth Prieto–Montañez, Prieto-Montañez, Yulieth · 1 citation
Mathematics · #14C05 #14D20 #14E05 #14J50 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2408.16610

openalex publication_date 2024/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

Inspired by well-known examples of hyperkähler manifolds, we show that any hyperkähler manifold X of K3^[n]-type with Picard number ρ(X) ≥ 4 is always isomorphic to a moduli space of twisted stable sheaves on a K3 surface. Additionally, we provide explicit descriptions of hyperkähler manifolds of K3^[n]-type with Picard ranks below this crucial value (e.g., ρ(X)=3) that are not birational to such moduli spaces.

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