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Math Help - Algebraic Geometry

  1. #1
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    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.
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  2. #2
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    Quote Originally Posted by Capillarian View Post
    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
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