Projective duality and K-energy asymptotics

Details Projective duality and K-energy asymptotics Projective duality and K-energy asymptotics

2008-11-16

arxiv.org/abs/0811.2544v1

Mathematics

Differential Geometry

27 pages

Scientific paper

Let X be a smooth, linearly normal n dimensional complex projective variety. Assume that the projective dual of X has codimension one with defining polynomial D(X). In this paper the log of the norm of D(X) is expressed as the restriction to the Bergman metrics of an energy functional on X. We show how, for smooth plane curves, this energy functional reduces to the standard action functionals of Kahler geometry.

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