K Energy and K stability on Hypersurfaces

Details K Energy and K stability on Hypersurfaces K Energy and K stability on Hypersurfaces

2001-08-02

arxiv.org/abs/math/0108009v1

Communications in Analysis and Geometry, vol 12(3), 2004, pp 599-628

Mathematics

Differential Geometry

Scientific paper

In this paper, we study the limiting properties of the $K$ energy for smooth hypersurfaces in the projective spaces. Our result generalizes the result of Ding-Tian (W. Ding and G. Tian. K\"ahler-Einstein metrics and the generalized Futaki invariant. {\em Invent Math}, 110:315-335, 1992.) in the case of hypersurfaces. In particular, we allow the center fiber of a special degeneration (a degeneration by a one-parameter group) to have multiplicity great than 1.

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