Segre numbers, a generalized King formula, and local intersections

Andersson, Mats, 1957 (author): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences

Samuelsson Kalm, Håkan, 1976 (author): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences

Wulcan, Elizabeth, 1978 (author): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences

(creator_code:org_t)

2015-01-15
2017
English.
In: Journal für die Reine und Angewandte Mathematik. - : Walter de Gruyter GmbH. - 1435-5345 .- 0075-4102. ; 728:728, s. 105-136

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Abstract Subject headings

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 theso-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 ofthe classical King formula that takes into account fixed and moving components of Vogelcycles associated with $\mathcal{J}$. A basic tool is a new calculus for products of positive currents ofBochner–Martinelli type. We also discuss connections to intersection theory.

By the author/editor: Andersson, Mats, ...; Samuelsson Kalm, ...; Wulcan, Elizabet ...; Yger, Alain

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Mathematical Ana ...

By the university: Chalmers University of Technology; University of Gothenburg

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