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

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

2008-03-02

arxiv.org/abs/0803.0136v1

Mathematics

Complex Variables

16 pages

Scientific paper

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 H\"older 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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