We generalize the classical Hilbert–Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X→ SpecA to a noetherian k-algebra A. We also extend the classical projectivity result for GIT quotients: the induced morphism (Formula presented.) SpecAG is projective. As an example of applications to moduli problems, we consider degenerations of Hilbert schemes of points.
Gulbrandsen M.G., Halle L.H., Hulek K. (2015). A relative Hilbert–Mumford criterion. MANUSCRIPTA MATHEMATICA, 148(3-4), 283-301 [10.1007/s00229-015-0744-8].
A relative Hilbert–Mumford criterion
Halle L. H.;
2015
Abstract
We generalize the classical Hilbert–Mumford criteria for GIT (semi-)stability in terms of one parameter subgroups of a linearly reductive group G over a field k, to the relative situation of an equivariant, projective morphism X→ SpecA to a noetherian k-algebra A. We also extend the classical projectivity result for GIT quotients: the induced morphism (Formula presented.) SpecAG is projective. As an example of applications to moduli problems, we consider degenerations of Hilbert schemes of points.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
