On irreducible symplectic 4-folds numerically equivalent to (K3)^[2]

2010/04/19 by Grzegorz Kapustka, Kapustka, Grzegorz
Mathematics · #14J35 #14J70 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1004.3177

openalex publication_date 2010/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We address the problem of classification of hyper-Kähler fourfolds with b₂=23. In particular we prove some special cases of the Conjecture of O'Grady about hyper-Kähler 4-folds numerically equivalent to the Hilbert scheme of two points on a K3 surface.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Related

• A characterization of certain irreducible symplectic 4-folds
• Irreducible symplectic 4-folds numerically equivalent to Hilb²(K3)
• Hyper-Kähler fourfolds and Grassmann geometry
• Calabi--Yau quotients of hyperkähler four-folds
• Higher-dimensional analogues of K3 surfaces