Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonal projection of a test configuration to vector fields   Given a polarized complex manifold, projection of a torus-equivariant test
configuration to holomorphic vector fields was introduced by G. Sz\'ekelyhidi,
as the limit of the associated $\mathbb{C}^*$-actions. We show that there
actually holds the moment convergence of the weight distributions. Our analytic
approach at the same time specifies the limit in terms of the weak geodesic ray
associated with the test configuration. Related to the result, we discuss about
the reduced $L^p$-norm of the test configuration in attempt to describe the
uniform K-stability of the polarization relative to the automorphism group.

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom