Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetric tensor rank with a tangent vector: a generic uniqueness
  theorem   Let $X_{m,d}\subset \mathbb {P}^N$, $N:= \binom{m+d}{m}-1$, be the order $d$
Veronese embedding of $\mathbb {P}^m$. Let $\tau (X_{m,d})\subset \mathbb
{P}^N$, be the tangent developable of $X_{m,d}$. For each integer $t \ge 2$ let
$\tau (X_{m,d},t)\subseteq \mathbb {P}^N$, be the joint of $\tau (X_{m,d})$ and
$t-2$ copies of $X_{m,d}$. Here we prove that if $m\ge 2$, $d\ge 7$ and $t \le
1 + \lfloor \binom{m+d-2}{m}/(m+1)\rfloor$, then for a general $P\in \tau
(X_{m,d},t)$ there are uniquely determined $P_1,...,P_{t-2}\in X_{m,d}$ and a
unique tangent vector $\nu$ of $X_{m,d}$ such that $P$ is in the linear span of
$\nu \cup \{P_1,...,P_{t-2}\}$, i.e. a degree $d$ linear form $f$ associated to
$P$ may be written as $$f = L_{t-1}^{d-1}L_t + \sum_{i=1}^{t-2} L_i^d$$ with
$L_i$, $1 \le i \le t$, uniquely determined (up to a constant) linear forms on
$\mathbb {P}^m$.

25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
14
The categories of this paper are: math-ph
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio