An explicit d-bar-integration formula for weighted homogeneous varieties

Jean Ruppenthal; Eduardo S. Zeron

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arXiv · 0803.0136

An explicit d-bar-integration formula for weighted homogeneous varieties

Jean Ruppenthal·Eduardo S. Zeron

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Abstract

Let Y be a weighted homogeneous (singular) subvariety of C^n. The main objective of this paper is to present an explicit formula for solving the d-bar-equation $f=\dbar{g}$ on the regular part of Y, where $f$ is a d-bar-closed $(0,1)$-form with compact support. This formula will then be used to give Hölder estimates for the solution in case $Y$ is homogeneous (a cone) with an isolated singularity. Finally, a slight modification of our formula also gives an $L^2$-bounded solution operator in case Y is pure dimensional and homogeneous.

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BibTeX RIS

Jean Ruppenthal, Eduardo S. Zeron. 2008-03-02. An explicit d-bar-integration formula for weighted homogeneous varieties. https://arxiv.org/abs/0803.0136

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