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, Volume 156, Issue 1–2, pp 63–80 | Cite as

A twisted \({\overline{\partial }}_{f}\)-Neumann problem and Toeplitz n-tuples from singularity theory

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Abstract

A twisted \(\bar{\partial }_f\)-Neumann problem associated to a singularity \((\mathscr {O}_n, f)\) is established. By relating it to the Koszul complex for Toeplitz n-tuples \((f_1,\ldots ,f_n)\), where \(f_i=\frac{\partial f}{\partial z_i}\), on Bergman space \(B^0(D)\), this \(\bar{\partial }_f\)-Neumann problem is solved. Moreover, the cohomology of the \(L^2\)-holomorphic Koszul complex \((B^*(D),{\partial }f\wedge )\) can be computed explicitly.

Mathematics Subject Classification

32W99 58K99 

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingChina

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