调和Higgs丛与余结合ALE纤维化

Rodrigo Barbosa

调和Higgs丛与余结合ALE纤维化

微分几何 2021-01-01 v2 高能物理 - 理论代数几何

作者: Rodrigo Barbosa

摘要

受弦对偶的启发，我们构造了 $G_2$ -orbifolds的形变族，这些orbifold作为余结合纤维化总空间，其底空间为闭定向光滑三维流形 $Q$ ，纤维为ADE奇点。形变由 $Q$ 上纤维丛的截面参数化，这些截面可解释为某些Higgs丛的黎曼类比相关的谱/cameral覆盖。谱覆盖图像是文献中出现的几种不同余结合纤维化方法的统一框架。我们的构造将著名的ADE纤维化Calabi-Yau三维流形族推广到 $G_2$ -几何语境，该族的形变由其底黎曼面上的全纯Higgs丛的谱覆盖参数化。

关键词

调和Higgs丛余结合纤维化 G_2-几何 ALE空间谱覆盖形变

引用

@article{arxiv.1910.10742,
  title  = {Harmonic Higgs Bundles and Coassociative ALE Fibrations},
  author = {Rodrigo Barbosa},
  journal= {arXiv preprint arXiv:1910.10742},
  year   = {2021}
}

备注

Main Theorem generalized to arbitrary closed orientable smooth three-manifolds. New section added with general construction of ADE-fibered $G_2$-orbifolds. Minor modifications: new subsection on the relation between D-term and the adiabatic limit; new subsections on cameral covers and twistor geometry. Corrected an error in the discussion on character varieties (which did not affect computations)

调和Higgs丛与余结合ALE纤维化

摘要

关键词

引用

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