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Green functions, Segre numbers, and King’s formula

Mats Andersson (Institutionen för matematiska vetenskaper, matematik) ; Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik)
Annales de l'Institut Fourier (0373-0956). Vol. 64 (2014), 6, p. 2639-2657.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Green function; Segre numbers; Monge-Ampere products; King's formula

Denna post skapades 2015-01-06. Senast ändrad 2016-04-28.
CPL Pubid: 209686


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