GREEN FUNCTIONS WITH SINGULARITIES ALONG COMPLEX SPACES
2005; World Scientific; Volume: 16; Issue: 04 Linguagem: Inglês
10.1142/s0129167x05002904
ISSN1793-6519
AutoresAlexander Rashkovskii, Ragnar Sigurðsson,
Tópico(s)Geometric Analysis and Curvature Flows
ResumoWe study properties of a Green function G A with singularities along a complex subspace A of a complex manifold X. It is defined as the largest negative plurisubharmonic function u satisfying locally u≤ log |ψ|+C, where ψ=(ψ 1 ,…,ψ m ), ψ 1 ,…,ψ m are local generators for the ideal sheaf ℐ A of A, and C is a constant depending on the function u and the generators. A motivation for this study is to estimate global bounded functions from the sheaf ℐ A and thus proving a "Schwarz lemma" for ℐ A .
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