2016/04/01 by Martin G. Gulbrandsen, Gulbrandsen, Martin G., Lars Halvard Halle +3 · 1 citation
Mathematics · Physics and Astronomy · #14C05 #14D06 (Primary) #14D23 (Secondary) #14L24 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1604.00215
openalex publication_date 2016/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a Geometric Invariant Theory (GIT) construction which allows us to construct good projective degenerations of Hilbert schemes of points for simple degenerations. A comparison with the construction of Li and Wu shows that our GIT stack and the stack they construct are isomorphic, as are the associated coarse moduli schemes. Our construction is sufficiently explicit to obtain good control over the geometry of the singular fibres. We illustrate this by giving a concrete description of degenerations of degree n Hilbert schemes of a simple degeneration with two components.