Rational Covariants of Reductive Groups and Homaloidal Polynomials
نویسندگان
چکیده
Let G be a complex reductive group, V a G-module and f ∈ O(V )G a nonconstant homogeneous invariant. We investigate relations between the following properties: • df : V → V ∗ is dominant, • f is homaloidal, i.e., df induces a birational map P(V ) → P(V ∗), • V is stable, i.e., the generic G-orbit is closed. If f generates O(V )G, we show that the properties are equivalent, generalizing results of Sato-Kimura on prehomogeneous vector spaces.
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