If the canonical class of "V" is an ample line bundle, then the canonical ring is the homogeneous coordinate ring of the image of the canonical map. This can be true even when the canonical class of "V" is not ample. For instance, if "V" is a hyperelliptic curve, then the canonical ring is again the homogeneous coordinate ring of the image of the canonical map. In general, if the ring above is finitely generated, then it is elementary to see that it is the homogeneous coordinate ring of the image of a "k"-canonical map, where "k" is any sufficiently divisible positive integer.