Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher secant varieties of $\mathbb{P}^n \times \mathbb{P}^m$ embedded
  in bi-degree $(1,d)$   Let $X^{(n,m)}_{(1,d)}$ denote the Segre-Veronese embedding of $\mathbb{P}^n
\times \mathbb{P}^m$ via the sections of the sheaf $\mathcal{O}(1,d)$. We study
the dimensions of higher secant varieties of $X^{(n,m)}_{(1,d)}$ and we prove
that there is no defective $s^{th}$ secant variety, except possibly for $n$
values of $s$. Moreover when ${m+d \choose d}$ is multiple of $(m+n+1)$, the
$s^{th}$ secant variety of $X^{(n,m)}_{(1,d)}$ has the expected dimension for
every $s$.

21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph