K Energy and K stability on Hypersurfaces

2001/08/02 by Zhiqin Lu
Mathematics · #math.DG #msc:53A30

paper · pdf

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

arxiv created 2001/08/02 · arxiv updated 2009/11/30

Abstract

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. Kähler-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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