Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-vanishing of the twisted cohomology on the complement of
  hypersurfaces   Under the generic situation, the cohomology with the coefficients in the
local system on complements of hypersurfaces vanishes except in the highest
dimension. Our problem is of when the local system cohomology does not vanish.
In the case of arrangements of hyperplanes, many examples were founded. In this
paper, we shall generalize their examples to hypersurfaces. We obtain that
hypersurfaces given by some linear system have non-vanishing local system
cohomologies.

8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph