Green functions, Segre numbers, and King’s formula
Journal article, 2014

Let 𝒥 be a coherent ideal sheaf on a complex manifold X with zero set Z, and let G be a plurisubharmonic function such that G=log|f|+𝒪(1) locally at Z, where f is a tuple of holomorphic functions that defines 𝒥. We give a meaning to the Monge-Ampère products (dd c G) k for k=0,1,2,..., and prove that the Lelong numbers of the currents M k 𝒥 :=1 Z (dd c G) k at x coincide with the so-called Segre numbers of J at x, introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that M k 𝒥 satisfy a certain generalization of the classical King formula.

Monge-Ampere products

Segre numbers

Green function

King's formula

Author

Mats Andersson

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Elizabeth Wulcan

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Annales de lInstitut Fourier

0373-0956 (ISSN)

Vol. 64 6 2639-2657

Subject Categories

Mathematics

Roots

Basic sciences

DOI

10.5802/aif.2922

More information

Created

10/7/2017