Segre numbers, a generalized King formula , and local intersections
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en
Document de travail - Pré-publication
Résumé en anglais
Let $J$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$. We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge-Amp ere products ($dd^c log |f|^2)^k$, where $f$ is a ...Lire la suite >
Let $J$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$. We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge-Amp ere products ($dd^c log |f|^2)^k$, where $f$ is a tuple of generators of $J$ , coincide with the so-called Segre numbers of $J$ , introduced independently by Tworzewski and Ga ffney-Gassler. More generally we show that these currents satisfya generalization of the classical King formula that takes into account fixed andmoving components of Vogel cycles associated with $J$ . A basic tool is a new calculusfor products of positive currents of Bochner-Martinelli type. We also discussconnections to intersection theory.< Réduire
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