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Classical Poincaré metric pulled back off singularities using a Chow-type theorem and desingularization

Caroline Grant MellesPierre Milman — 2006

Annales de la faculté des sciences de Toulouse Mathématiques

We construct complete Kähler metrics on the nonsingular set of a subvariety X of a compact Kähler manifold. To that end, we develop (i) a constructive method for replacing a sequence of blow-ups along smooth centers, with a single blow-up along a product of coherent ideals corresponding to the centers and (ii) an explicit local formula for a Chern form associated to this ‘singular’ blow-up. Our metrics have a particularly simple local formula of a sum of the original metric and of the pull back...

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