PreprintarXiv licencearXiv
Vanishing theorems for L2 Dolbeault cohomology groups of projective Hartogs triangles
Abstract
In this note, using J.-P. Demailly's L2 existence theorem for possibly incomplete Kähler metrics, we establish L2 estimates and vanishing theorems for a class of domains in ℙn without any boundary regularity assumptions. In particular, we give an affirmative answer to M.-C. Shaw's question concerning the vanishing of the L2 Dolbeault cohomology groups of projective Hartogs triangles.
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BibTeX
@misc{chen2026vanishing,
title = {{Vanishing theorems for $L^2$ Dolbeault cohomology groups of projective Hartogs triangles}},
author = {Jian Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37572},
eprint = {2610.37572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37572},
}
RIS
TY - UNPB
TI - Vanishing theorems for L^2 Dolbeault cohomology groups of projective Hartogs triangles
AU - Jian Chen
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37572
UR - https://arxiv.org/abs/2610.37572
AB - 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 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.
ER -