I'll be honest, I am not quite sure what this question is getting at:
Q: Show that dimension is an invariant of the isomorphism class of a projective variety.
If they are really talking about the class of objects isomorphic to this projective variety, then surely this statement is obvious? Help would be greatly appreciated.
Originally Posted by Capillarian
If I remember right, the dimension of a variety V is the trascendence degree of
the fractions field of the variety's coordinate ring K[V] over K , and since isomorphic
varieties have isomorphic coordinate rings we are thus done...I think.