Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some Fano manifolds admitting a rational fibration   Let X be a smooth, complex Fano variety. For every prime divisor D in X, we
set c(D):=dim ker(r:H^2(X,R)->H^2(D,R)), where r is the natural restriction
map, and we define an invariant of X as c_X:=max{c(D)|D is a prime divisor in
X}. In a previous paper we showed that c_X<9, and that if c_X>2, then either X
is a product, or X has a flat fibration in Del Pezzo surfaces. In this paper we
study the case c_X=2. We show that up to a birational modification given by a
sequence of flips, X has a conic bundle structure, or an equidimensional
fibration in Del Pezzo surfaces. We also show a weaker property of X when
c_X=1.

18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn