Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Arithmetic properties of the first secant variety to a projective
  variety   Under an explicit positivity condition, we show the first secant variety of a
linearly normal smooth variety is projectively normal, give results on the
regularity of the ideal of the secant variety, and give conditions on the
variety that are equivalent to the secant variety being arithmetically
Cohen-Macaulay. Under this same condition, we then show that if $X$ satisfies
$N_{p+2\dim(X)}$, then the secant variety satisfies $N_{3,p}$.

33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph