Let be a coherent ideal sheaf on a complex manifold with zero set , and let be a plurisubharmonic function such that locally at , where is a tuple of holomorphic functions that defines . We give a meaning to the Monge-Ampère products for , and prove that the Lelong numbers of the currents at coincide with the so-called Segre numbers of at , introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that satisfy a certain generalization of the classical King formula.
Soit un faisceau cohérent d’ideaux sur un variété complexe lisse , et soit la variété de . Soit une fonction plurisousharmonique telle que localement sur , où est un -uple de fonctions holomorphes qui définit . Nous donnons un sens au produit de Monge-Ampère pour , et nous montrons que les nombres de Lelong des courants en coïncident avec les nombres de Segre de en , introduits indépendemment par Tworzewski, Gaffney-Gassler et Achilles-Manaresi. Plus généralement, nous montrons que les satisfont une certaine généralisation de la formule de King.
Keywords: Green function, Segre numbers, Monge-Ampère products, King’s formula
Mot clés : Fonctions de Green, nombres de Segre, produits de Monge-Ampère, formule de King
Andersson, Mats 1; Wulcan, Elizabeth 1
@article{AIF_2014__64_6_2639_0, author = {Andersson, Mats and Wulcan, Elizabeth}, title = {Green functions, {Segre} numbers, and {King{\textquoteright}s} formula}, journal = {Annales de l'Institut Fourier}, pages = {2639--2657}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {64}, number = {6}, year = {2014}, doi = {10.5802/aif.2922}, mrnumber = {3331176}, zbl = {06387349}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2922/} }
TY - JOUR AU - Andersson, Mats AU - Wulcan, Elizabeth TI - Green functions, Segre numbers, and King’s formula JO - Annales de l'Institut Fourier PY - 2014 SP - 2639 EP - 2657 VL - 64 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2922/ DO - 10.5802/aif.2922 LA - en ID - AIF_2014__64_6_2639_0 ER -
%0 Journal Article %A Andersson, Mats %A Wulcan, Elizabeth %T Green functions, Segre numbers, and King’s formula %J Annales de l'Institut Fourier %D 2014 %P 2639-2657 %V 64 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2922/ %R 10.5802/aif.2922 %G en %F AIF_2014__64_6_2639_0
Andersson, Mats; Wulcan, Elizabeth. Green functions, Segre numbers, and King’s formula. Annales de l'Institut Fourier, Volume 64 (2014) no. 6, pp. 2639-2657. doi : 10.5802/aif.2922. https://aif.centre-mersenne.org/articles/10.5802/aif.2922/
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