Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric vertex decomposition and liaison   Geometric vertex decomposition and liaison are two frameworks that have been
used to produce similar results about similar families of algebraic varieties.
In this paper, we establish an explicit connection between these approaches. In
particular, we show that each geometrically vertex decomposable ideal is linked
by a sequence of elementary G-biliaisons of height 1 to an ideal of
indeterminates and, conversely, that every G-biliaison of a certain type gives
rise to a geometric vertex decomposition. As a consequence, we can immediately
conclude that several well-known families of ideals are glicci, including
Schubert determinantal ideals, defining ideals of varieties of complexes, and
defining ideals of graded lower bound cluster algebras.

16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org