非 Kähler 流形上的稳定 Higgs 丛与 Hermitian-Einstein 度量
微分几何
2014-10-28 v2
摘要
设 X 为紧致 Gauduchon 流形，E 和 V_0 为 X 上的全纯向量丛。假设在考虑 Higgs 场 θ∈H^0(End(E)⊗V_0) 保持的所有子层时 E 是稳定的。则修正的 Donaldson 热流沿某一子列时间收敛到广义 Hermitian-Einstein 方程的解，该方程为 iΛF+[θ,θ^†]=λI。
引用
@article{arxiv.1110.3768,
title = {Stable Higgs bundles and Hermitian-Einstein metrics on non-K\"ahler manifolds},
author = {Adam Jacob},
journal= {arXiv preprint arXiv:1110.3768},
year = {2014}
}
备注
The main theorem has been extended to the case of Higgs pairs. Several errors have been corrected, and new references have been added, as suggested by the referee. Final version to appear in Analysis, Complex Geometry, and Mathematical Physics: A conference in honor of D. H. Phong, Contemporary Mathematics, American Mathematical Society. 25 pages