Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birational geometry of defective varieties, II   Let $X \subset \mathbb{P}^r$ be smooth and irreducible and for $k \ge 0$ let
$\nu_k(X)$ (resp., $\delta_k(X)$) be the $k$-th contact (resp., the $k$-th
secant) defect of $X$. For all $k \ge 0$ we have the inequality $\nu_k(X) \ge
\delta_k(X)$ and in the case $k=1$ we characterize projective varieties $X$ for
which equality holds, $\dim \mathrm{Sing}(X) \le \delta _1(X) -1$ and the
generic tangential contact locus is reducible.

31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat