Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A study of the Hilbert-Mumford criterion for the stability of projective
  varieties   We make a systematic study of the Hilbert-Mumford criterion for different
notions of stability for polarised algebraic varieties $(X,L)$; in particular
for K- and Chow stability. For each type of stability this leads to a concept
of slope $\mu$ for varieties and their subschemes; if $(X,L)$ is semistable
then $\mu(Z)\le\mu(X)$ for all $Z\subset X$. We give examples such as curves,
canonical models and Calabi-Yaus. We prove various foundational technical
results towards understanding the converse, leading to partial results; in
particular this gives a geometric (rather than combinatorial) proof of the
stability of smooth curves.

18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th