Geodesic
A GIT Construction of Degenerations of Hilbert Schemes of Points
Documenta mathematica, Tome 24 (2019), pp. 421-472
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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 n Hilbert schemes of a simple degeneration with two components.
DOI : 10.4171/dm/685
Classification : 14C05, 14D06, 14D23, 14L24
Mots-clés : Hilbert scheme, GIT, Hilbert scheme of points, geometric invariant theory, Donaldson-Thomas invariants, degeneration, expanded degenerations, Pandharipande-Thomas stable pairs, K3 surfaces, Li-Wu stack, bipartite graph, smooth support, numerical support, GIT quotient, stack quotient, Deligne-Mumford stack 
@article{10_4171_dm_685,
     author = {Martin G. Gulbrandsen and Lars H. Halle and Klaus Hulek},
     title = {A {GIT} {Construction} of {Degenerations} of {Hilbert} {Schemes} of {Points}},
     journal = {Documenta mathematica},
     pages = {421--472},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/685},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/685/}
}
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Martin G. Gulbrandsen; Lars H. Halle; Klaus Hulek. A GIT Construction of Degenerations of Hilbert Schemes of Points. Documenta mathematica, Tome 24 (2019), pp. 421-472. doi: 10.4171/dm/685

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