PreprintarXiv licencearXiv
Stability of representation cohomology sheaves on moduli spaces of bundles
Abstract
We prove that the tangent sheaf of SUC(n,L) is slope stable for every smooth complex projective curve C of genus g≥2, every n≥2, and every determinant L. For g≥3, we prove a more general stability theorem on moduli spaces of principal bundles for connected reductive groups, using cohomology sheaves associated with representations in place of tangent sheaves. The adjoint representation gives tangent sheaf stability for the case of almost simple groups. The moduli spaces may be singular, and stability holds with respect to every ample Cartier polarization.
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BibTeX
@misc{wang2026stability,
title = {{Stability of representation cohomology sheaves on moduli spaces of bundles}},
author = {Jianping Wang and Xueqing Wen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01481},
eprint = {2610.01481},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01481},
}
RIS
TY - UNPB
TI - Stability of representation cohomology sheaves on moduli spaces of bundles
AU - Jianping Wang
AU - Xueqing Wen
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01481
UR - https://arxiv.org/abs/2610.01481
AB - We prove that the tangent sheaf of SU_C(n,L) is slope stable for every smooth complex projective curve C of genus g≥2, every n≥2, and every determinant L. For g≥3, we prove a more general stability theorem on moduli spaces of principal bundles for connected reductive groups, using cohomology sheaves associated with representations in place of tangent sheaves. The adjoint representation gives tangent sheaf stability for the case of almost simple groups. The moduli spaces may be singular, and stability holds with respect to every ample Cartier polarization.
ER -