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A GIT construction of degenerations of Hilbert schemes of points

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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.
OriginalsprogEngelsk
TidsskriftDocumenta Mathematica
Vol/bind24
Sider (fra-til)421-472
Antal sider52
ISSN1431-0635
DOI
StatusUdgivet - 2019

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