Inducing coverings on Hilbert schemes

2025/06/27 by Bassi, Lucas Li, Papallo, Filippo
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.22031

Abstract

We find an explicit geometric description of all coverings of the Hilbert square on a normal, complex, quasi-projective surface with finite fundamental group. We then apply this construction to show that if Σ is an irreducible symplectic surface then its Hilbert square is an irreducible symplectic variety.

Citations

• The Hilbert schemes of points on surfaces with rational double point singularities
• Universal covering calabi-yau manifolds of the Hilbert schemes of n points of Enriques surfaces
• Enriques manifolds
• Q.E.D. for algebraic varieties
• Extension of 2-forms and symplectic varieties
• Algebraic Families on an Algebraic Surface

Related

• Singular symplectic surfaces
• Pathologies of Hilbert scheme of points of supersingular Enriques\n surface
• The Hilbert schemes of points on surfaces with rational double point singularities
• A characterization of certain irreducible symplectic 4-folds
• Hilbert schemes of points on surfaces