Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Valuative invariants with higher moments   In this article we introduce a family of valuative invariants defined in
terms of the $p$-th moment of the expected vanishing order. These invariants
lie between $\alpha$ and $\delta$-invariants. They vary continuously in the big
cone and semi-continuously in families. Most importantly, they can detect the
K-stability of Fano varieties, which generalizes the $\alpha$ and
$\delta$-criterions in the literature. They are also related to the
$d_p$-geometry of maximal geodesic rays.

29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph