Mathematical Research Letters

Volume 8 (2001)

Number 6

The map $V\longrightarrow V/\!/G$ need not be separable

Pages: 813 – 817



Ben Martin (The Hebrew University)

Amnon Neeman (The Australian National University)


We construct a vector space $V$ with a linear action of a reductive group $G$ such that the quotient map $V \longrightarrow V/\!/G$ (in the sense of geometric invariant theory) fails to be separable. This gives a counterexample to an assertion of Bardsley and Richardson.

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