1. Algebraic Geometry

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.

2. Originally Posted by Capillarian
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.

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.

Tonio