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On Hyperk\"ahler manifolds of K3$^{[n]}$-type with large Picard number

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arxiv 2408.16610 v2 pith:3U4LJQU3 submitted 2024-08-29 math.AG math.NT

classification math.AGmath.NT
keywords ahlerhyperkmanifoldspicardtypemodulinumberadditionally
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abstract

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

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Zeta functions of K3 categories over finite fields

    math.AG 2025-05 conditional novelty 8.0 of 10

    Noncommutative K3 surfaces over finite fields get zeta functions whose point counts can be negative, obstruct geometricity, and in one explicit example, perfectly mimic a K3 surface without being geometric.

  2. Correspondences for hyperk\"ahler varieties with large Picard numbers

    math.AG 2026-07 accept novelty 5.0 of 10

    Projective hyperkähler manifolds of K3^[n] type with T(X)⊗Q embedding into U³⊗Q admit algebraic correspondences to abelian varieties inducing Hodge isometries of transcendental lattices.

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