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Segre numbers, a generalized King formula, and local intersections

Mats Andersson (Institutionen för matematiska vetenskaper, matematik) ; Håkan Samuelsson (Institutionen för matematiska vetenskaper, matematik) ; Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik) ; Alain Yger
Journal für die Reine und Angewandte Mathematik (0075-4102). Vol. 728 (2015), p. 105-136 .

Let $\mathcal{J}$ 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– Ampère products $(dd^c \log |f|^2)^k$, where $f$ is a tuple of generators of $\mathcal{J}$, coincide with the so-called Segre numbers of $\mathcal{J}$, introduced independently by Tworzewski, Achilles–Manaresi, and Gaffney–Gassler. More generally we show that these currents satisfy a generalization of the classical King formula that takes into account fixed and moving components of Vogel cycles associated with $\mathcal{J}$. A basic tool is a new calculus for products of positive currents of Bochner–Martinelli type. We also discuss connections to intersection theory.

http://arxiv.org/abs/1009.2458

CPL Pubid: 227957

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)