Green functions with singularities along complex spaces

Details Green functions with singularities along complex spaces Green functions with singularities along complex spaces

2004-08-30

arxiv.org/abs/math/0408407v1

Mathematics

Complex Variables

22 pages

Scientific paper

We 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\leq \log|\psi|+C, where \psi=(\psi_1, ...,\psi_m), \psi_1, ...,\psi_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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