isomorphism of varieties

Definition 1.

Let V1 and V2 be algebraic varieties. We say that V1 and V2 are isomorphic, and write V1V2, if there are regular maps


such that the compositionsMathworldPlanetmathPlanetmath ψϕ and ϕψ are the identity maps on V1 and V2 respectively.

Definition 2.

Let V1 and V2 be varietiesMathworldPlanetmathPlanetmath defined over a field K. We say that V1/K and V2/K are isomorphic over K if V1 and V2 are isomorphic as in Definition 1 and the regular maps ϕ and ψ can be defined over K.

Title isomorphism of varieties
Canonical name IsomorphismOfVarieties
Date of creation 2013-03-22 15:06:22
Last modified on 2013-03-22 15:06:22
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 4
Author alozano (2414)
Entry type Definition
Classification msc 14A10
Related topic JInvariantClassifiesEllipticCurvesUpToIsomorphism