  Let X be a smooth projective variety and let K be the canonical divisor of X.
In this paper, we study embeddings of X given by adjoint line bundles of the
form K+L, where L is an ample line bundle. When X is a regular surface (i.e.
H^1(X, O_X) = 0), we obtain a numerical criterion for K+L to have property Np.
When X is a regular variety of arbitrary dimension, under a mild condition, we
give an explicit calculation for the regularity of the ideal sheaves of such
embeddings.
