The d-bar-equation on homogeneous varieties with an isolated singularity

Details The d-bar-equation on homogeneous varieties with an isolated singularity The d-bar-equation on homogeneous varieties with an isolated singularity

2008-03-09

arxiv.org/abs/0803.1188v3

Mathematics

Complex Variables

35 pages; extended introduction, new references

Scientific paper

Let X be a regular irreducible variety in CP^{n-1}, Y the associated homogeneous variety in C^n, and N the restriction of the universal bundle of CP^{n-1} to X. In the present paper, we compute the obstructions to solving the d-bar-equation in the L^p-sense on Y for 1<=p<=\infty in terms of cohomology groups H^q(X,O(N^m)). That allows to identify obstructions explicitly if X is specified more precisely, for example if it is equivalent to CP^1 or an elliptic curve.

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