A Remark on the Gradient Map

For a Hamiltonian action of a compact group $U$ of isometries on a compact Kähler manifold $Z$ and a compatible subgroup $G$ of $U^\C$, we prove that for any closed $G$--invariant subset $Y\subset Z$ the image of the gradient map $\mup(Y)$ is independent of the choice of the invariant Kähler form $\om$ in its cohomology class $[\om]$.

2010 Mathematics Subject Classification: 53D20

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