Segre numbers, a generalized King formula, and local intersections
Journal article, 2015

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.

Author

Mats Andersson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Håkan Samuelsson Kalm

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Elizabeth Wulcan

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Alain Yger

University of Bordeaux

Journal für die Reine und Angewandte Mathematik

0075-4102 (ISSN)

Vol. 728 728 105-136

Subject Categories

Mathematics

Geometry

Mathematical Analysis

DOI

10.1515/crelle-2014-0109

More information

Latest update

2/28/2018