English

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

Complex Variables 2009-03-24 v3

Abstract

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.

Cite

@article{arxiv.0803.1188,
  title  = {The d-bar-equation on homogeneous varieties with an isolated singularity},
  author = {Jean Ruppenthal},
  journal= {arXiv preprint arXiv:0803.1188},
  year   = {2009}
}

Comments

35 pages; extended introduction, new references

R2 v1 2026-06-21T10:19:45.036Z