Symplectic stability, analytic stability in non-algebraic complex geometry

Details Symplectic stability, analytic stability in non-algebraic complex geometry Symplectic stability, analytic stability in non-algebraic complex geometry

2003-09-14

arxiv.org/abs/math/0309230v2

Mathematics

Complex Variables

LaTeX, 31 pages, Comments are welcome. March 02, 2004: Corrections of minor nature. To appear in Int. J. Math

Scientific paper

We give a systematic presentation of the stability theory in the non-algebraic Kaehlerian geometry. We introduce the concept of "energy complete Hamiltonian action". To an energy complete Hamiltonian action of a reductive group G on a complex manifold one can associate a G-equivariant maximal weight function and prove a Hilbert criterion for semistability. In other words, for such actions, the symplectic semistability and analytic semistability conditions are equivalent.

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