A GIT construction of degenerations of Hilbert schemes of points

TY - JOUR

T1 - A GIT construction of degenerations of Hilbert schemes of points

AU - Gulbrandsen, Martin G.

AU - Halle, Lars Halvard

AU - Hulek, Klaus

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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 ourGIT 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.

AB - 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 ourGIT 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.

U2 - 10.25537/dm.2019v24.421-472

DO - 10.25537/dm.2019v24.421-472

M3 - Journal article

SN - 1431-0635

VL - 24

SP - 421

EP - 472

JO - Documenta Mathematica

JF - Documenta Mathematica

ER -