Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Depth of an initial ideal   Given an arbitrary integer $d>0$, we construct a homogeneous ideal $I$ of the
polynomial ring $S = K[x_1, \ldots, x_{3d}]$ in $3d$ variables over a filed $K$
for which $S/I$ is a Cohen--Macaulay ring of dimension $d$ with the property
that, for each of the integers $0 \leq r \leq d$, there exists a monomial order
$<_r$ on $S$ with ${\rm depth} (S/{\rm in}_{<_r}(I)) = r$, where ${\rm
in}_{<_r}(I)$ is the initial ideal of $I$ with respect to $<_r$.

31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
3
The categories of this paper are: physics