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arXiv · 2610.37572

Vanishing theorems for $L^2$ Dolbeault cohomology groups of projective Hartogs triangles

Jian Chen
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Abstract

In this note, using J.-P. Demailly's $L^2$ existence theorem for possibly incomplete Kähler metrics, we establish $L^2$ estimates and vanishing theorems for a class of domains in $\mathbb P^n$ without any boundary regularity assumptions. In particular, we give an affirmative answer to M.-C. Shaw's question concerning the vanishing of the $L^2$ Dolbeault cohomology groups of projective Hartogs triangles.

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Jian Chen. 2026-10-27. Vanishing theorems for $L^2$ Dolbeault cohomology groups of projective Hartogs triangles. https://arxiv.org/abs/2610.37572

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