Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding codimension of the space of arcs   We introduce a notion of embedding codimension of an arbitrary local ring,
establish some general properties, and study in detail the case of arc spaces
of schemes of finite type over a field. Viewing the embedding codimension as a
measure of singularities, our main result can be interpreted as saying that the
singularities of the arc space are maximal at the arcs that are fully embedded
in the singular locus of the underlying scheme, and progressively improve as we
move away from said locus. As an application, we complement a theorem of
Drinfeld, Grinberg, and Kazhdan on formal neighborhoods in arc spaces by
providing a converse to their theorem, an optimal bound for the embedding
codimension of the formal model appearing in the statement, a precise formula
for the embedding dimension of the model constructed in Drinfeld's proof, and a
geometric meaningful way of realizing the decomposition stated in the theorem.

20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th