Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A relative Hilbert-Mumford criterion   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 ->
Spec A to a noetherian k-algebra A. We also extend the classical projectivity
result for GIT quotients: the induced morphism X^ss/G -> Spec A^G is
projective. As an example of applications to moduli problems, we consider
degenerations of Hilbert schemes of points.

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The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org