Solving $\overline\partial$ with prescribed support on Hartogs triangles in $\mathbb C^2$ and $\mathbb C\mathbb P^2$

Christine Laurent-Thiébaut; Mei-Chi Shaw

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arXiv · 1609.04194

Solving $\overline\partial$ with prescribed support on Hartogs triangles in $\mathbb C^2$ and $\mathbb C\mathbb P^2$

Christine Laurent-Thiébaut·Mei-Chi Shaw

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Abstract

In this paper we study the solvability of the Cauchy-Riemann equation with prescibed support in different spaces of forms. The unbounded Hartogs triangle in $\mathbb C^2$ and the Hartogs domains in $\mathbb C\mathbb P^2$ provide us new unexpected phenomena. In particular we prove that the Dolbeault isomorphism fails to hold for the Dolbeault cohomology with prescribed support

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Christine Laurent-Thiébaut, Mei-Chi Shaw. 2016-09-14. Solving $\overline\partial$ with prescribed support on Hartogs triangles in $\mathbb C^2$ and $\mathbb C\mathbb P^2$. https://arxiv.org/abs/1609.04194

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