Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On explicit birational geometry for minimal n-folds of canonical
  dimension n-1   Let $n\geq 2$ be any integer. We study the optimal lower bound $v_{n, n-i}$
of the canonical volume and the optimal upper bound $r_{n,n-i}$ of the
canonical stability index for minimal projective $n$-folds of general type,
which are canonically fibered by $i$-folds ($i=0,1$). The results for $i = 0$,
$v_{n,n}=2$ and $r_{n, n}=n+2$, are known to experts. In this article, we show
that $v_{n,n-1}=\frac{6}{2n+(n \bmod 3)}$ and $r_{n,n-1}=\frac{1}{3}(5n+ 3 + (n
\bmod 3))$. The machinery is applicable to all canonical dimensions $n-i$.

20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ