Symplectic stability, analytic stability in non-algebraic complex geometry
Complex Variables
2007-05-23 v2 Algebraic Geometry
Symplectic Geometry
Abstract
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.
Cite
@article{arxiv.math/0309230,
title = {Symplectic stability, analytic stability in non-algebraic complex geometry},
author = {Andrei Teleman},
journal= {arXiv preprint arXiv:math/0309230},
year = {2007}
}
Comments
LaTeX, 31 pages, Comments are welcome. March 02, 2004: Corrections of minor nature. To appear in Int. J. Math