Segre numbers, a generalized King formula, and local intersections
Artikel i vetenskaplig tidskrift, 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.

Författare

Mats Andersson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Håkan Samuelsson Kalm

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Elizabeth Wulcan

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Alain Yger

Universite de Bordeaux

Journal für die Reine und Angewandte Mathematik

0075-4102 (ISSN)

Vol. 728 105-136

Ämneskategorier

Matematik

Geometri

Matematisk analys

DOI

10.1515/crelle-2014-0109