Green functions, Segre numbers, and King’s formula
Artikel i vetenskaplig tidskrift, 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

Författare

Mats Andersson

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Elizabeth Wulcan

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Matematik

Annales de lInstitut Fourier

0373-0956 (ISSN)

Vol. 64 6 2639-2657

Ämneskategorier

Matematik

Fundament

Grundläggande vetenskaper

DOI

10.5802/aif.2922