Explicit Construction of Complete Kahler Metrics of Saper Type by Desingularization

Details Explicit Construction of Complete Kahler Metrics of Saper Type by Desingularization Explicit Construction of Complete Kahler Metrics of Saper Type by Desingularization

1999-07-09

arxiv.org/abs/math/9907056v2

Mathematics

Algebraic Geometry

amstex, 43 pages, corrected example pp 41 - 42

Scientific paper

We construct complete Kahler metrics of Saper type on the nonsingular set of a subvariety X of a compact Kahler manifold using (a) a method for replacing a sequence of blow-ups along smooth centers, used to resolve the singularities of X, with a single blow-up along a product of coherent ideals corresponding to the centers and (b) an explicit local formula for a Chern form associated to this single blow-up. Our metrics have a particularly simple local formula, involving essentially a product of distances to the centers of the blow-ups used to resolve the singularities of X. Our proof of (a) uses a generalization of Chow's theorem for coherent ideals, proved using the Direct Image Theorem.

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