  Let $(X,L)$ be an $n$-dimensional polarized variety. Fujita's conjecture says
that if $L^n>1$ then the adjoint bundle $K_X+nL$ is spanned and $K_X+(n+1)L$ is
very ample. There are some examples such that $K_X+nL$ is not spanned or
$K_X+(n+1)L$ is not very ample. These are $(\P^n,\O(1))$, hypersurface $M$ of
degree $6$ in weighted projective space $\P(3,2,1,1,\cdots ,1)$ with $\O_M(1)$
and numerically Godeaux surface etc. Numerically Godeaux surface is the
quotient space of a Fermat type hypersurface of degree $5$ in $\P^3$ by an
action of order $5$. These examples are not so much. We construct new examples
for any dimention.
