K Energy and K stability on Hypersurfaces
Zhiqin Lu
TL;DR
This paper investigates the limiting behavior of the K energy on smooth hypersurfaces in projective spaces, extending previous results to include cases with higher multiplicity in degenerations, thus broadening understanding of stability conditions.
Contribution
It generalizes Ding-Tian's results by analyzing K energy limits on hypersurfaces with degenerations having multiplicities greater than one.
Findings
Extended the understanding of K energy limits to hypersurfaces with complex degenerations.
Provided new insights into stability conditions for hypersurfaces in algebraic geometry.
Abstract
In this paper, we study the limiting properties of the 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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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory