  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.
