  Let X be a smooth complex projective variety of dimension n and let A be an
ample and basepoint free divisor. We prove $K_X+mA$ satisfies property $N_p$
for $m\geqslant n+1+p$. We also show the graded ring of sections $R(X, K_X+mA)$
is Koszul for $m\geqslant n+2$.
