Toric plurisubharmonic functions and analytic adjoint ideal sheaves

Details Toric plurisubharmonic functions and analytic adjoint ideal sheaves Toric plurisubharmonic functions and analytic adjoint ideal sheaves

2010-11-13

arxiv.org/abs/1011.3162v2

Mathematics

Complex Variables

24 pages, v2: A minor error fixed in the proof of Theorem 2.13, Two errors partially fixed: coherence of the adjoint ideal nee

Scientific paper

In the first part of this paper, we study the properties of some particular plurisubharmonic functions, namely the toric ones. The main result of this part is a precise description of their multiplier ideal sheaves, which generalizes the algebraic case studied by Howald. In the second part, almost entirely independent of the first one, we generalize the notion of the adjoint ideal sheaf used in algebraic geometry to the analytic setting. This enables us to give an analogue of Howald's theorem for adjoint ideals attached to monomial ideals. Finally, using the local Ohsawa-Takegoshi-Manivel theorem, we prove the existence of the so-called generalized adjunction exact sequence, which enables us to recover a weak version of the global extension theorem of Manivel, for compact K\"ahler manifolds.

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