  In this article we prove new results on projective normality and normal
presentation of adjunction bundle associated to an ample and globally generated
line bundle on higher dimensional smooth projective varieties with nef
canonical bundle. As one of the consequences of the main theorem, we give
bounds on very ampleness and projective normality of pluricanonical linear
systems on varieties of general type in dimensions three, four and five. These
improve known such results.
