A GIT construction of degenerations of Hilbert schemes of points
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A GIT construction of degenerations of Hilbert schemes of points. / Gulbrandsen, Martin G.; Halle, Lars Halvard; Hulek, Klaus.
In: Documenta Mathematica, Vol. 24, 2019, p. 421-472.Research output: Contribution to journal › Journal article › Research › peer-review
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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
Y1 - 2019
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 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 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 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 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
VL - 24
SP - 421
EP - 472
JO - Documenta Mathematica
JF - Documenta Mathematica
SN - 1431-0635
ER -
ID: 189316485