Geodesic
A GIT Construction of Degenerations of Hilbert Schemes of Points
Documenta mathematica, Tome 24 (2019), pp. 421-472.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14D06, 14C05, 14L24, 14D23
Keywords: GIT, geometric invariant theory, degeneration, Hilbert scheme, expanded degenerations, Donaldson-Thomas invariants, Pandharipande-Thomas stable pairs, $K3$ surfaces, Hilbert scheme of points, Li-Wu stack, bipartite graph, smooth support, numerical support, GIT quotient, stack quotient, Deligne-Mumford stack 
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     author = {Gulbrandsen, Martin G. and Halle, Lars H. and Hulek, Klaus},
     title = {A {GIT} {Construction} of {Degenerations} of {Hilbert} {Schemes} of {Points}},
     journal = {Documenta mathematica},
     pages = {421--472},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a50/}
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Gulbrandsen, Martin G.; Halle, Lars H.; Hulek, Klaus. A GIT Construction of Degenerations of Hilbert Schemes of Points. Documenta mathematica, Tome 24 (2019), pp. 421-472. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a50/