K Energy and K stability on Hypersurfaces

Zhiqin Lu

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K Energy and K stability on Hypersurfaces

Zhiqin Lu

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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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Zhiqin Lu. 2001-08-02. K Energy and K stability on Hypersurfaces. https://arxiv.org/abs/math/0108009

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