Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entry loci and ranks   We study entry loci of varieties and their irreducibility from the
perspective of $X$-ranks with respect to a projective variety $X$. These loci
are the closures of the points that appear in an $X$-rank decomposition of a
general point in the ambient space. We look at entry loci of low degree normal
surfaces in $\mathbb P^4$ using Segre points of curves; the smooth case was
classically studied by Franchetta. We introduce a class of varieties whose
generic rank coincides with the one of its general entry locus, and show that
any smooth and irreducible projective variety admits an embedding with this
property.

37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th