Stability, Energy Functionals, and Kähler-Einstein Metrics

In this paper, building on the earlier work of Yau [Y3, Y4], Tian [T1,T2] and Zhang [Z], we construct a semi-norm ∥∙ ∥_# which is defined on the full space H⁰(Gr,O(d)) of polynomials of degree d on the Grassmann variety Gr, and which gives exactly the Mabuchi functional when restricted to the space of Chow vectors, up to a specific current supported on the singular locus of the Chow variety.

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Published 1 January 2003