发表机构
Tsinghua University; Yanqi Lake Beijing Institute of Mathematical Sciences and Applications（清华大学; 北京雁栖湖应用数学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究非线性调和丛中希格斯截面与平坦截面关系，证明一般情况下二者等价需次数障碍消失，还通过将态射解释为图子纤维化，把结果扩展到子纤维化和态射。
AI 中文摘要
我们在非线性调和丛的背景下研究希格斯截面、平坦截面及其高维与函子类似物。对于紧致凯勒流形上的调和向量丛，一个整体截面是平坦的当且仅当它是希格斯截面。我们表明对于一般的非线性调和丛，这种等价性需要一个次数障碍的消失。然后我们通过将态射解释为纤维积中的图子纤维化，将结果扩展到子纤维化和态射。
英文摘要
We establish a nonlinear Bochner-Kodaira-Nakano identity for sections of complex fiber bundles. As applications, we obtain a nonlinear Bochner-type vanishing theorem for holomorphic sections and a generalization of Yau's Schwarz lemma. After incorporating a nonlinear Higgs field, we derive the $D'$-$D''$ and $D^c$-$D$ identities. Under natural Hamiltonian and compactness assumptions, these identities imply that a section of a nonlinear harmonic bundle is flat if and only if it is a Higgs section with vanishing degree. We extend this correspondence first to sub-fibrations and then, via the graph construction, to morphisms.
Comments73 pages, comments welcome
