For a Hamiltonian action of a compact group U of isometries on a compact Kähler manifold Z and a compatible subgroup G of UC, we prove that for any closed G-invariant subset Y ⊂ Z the image of the gradient map μp(Y) is independent of the choice of the invariant Kähler form ω in its cohomology class [ω].
Biliotti, L., Ghigi, A., Heinzner, P. (2014). A remark on the gradient map. DOCUMENTA MATHEMATICA, 19(2014), 1017-1024.
A remark on the gradient map
GHIGI, ALESSANDRO CALLISTOSecondo
;
2014
Abstract
For a Hamiltonian action of a compact group U of isometries on a compact Kähler manifold Z and a compatible subgroup G of UC, we prove that for any closed G-invariant subset Y ⊂ Z the image of the gradient map μp(Y) is independent of the choice of the invariant Kähler form ω in its cohomology class [ω].
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