论文标题
Bialynicki-birula理论，莫尔斯 - 博特理论和分析空间的奇异性的分辨率
Bialynicki-Birula theory, Morse-Bott theory, and resolution of singularities for analytic spaces
论文作者
论文摘要
我们在这项工作中的目标是开发Bialynicki-Birula和Morse-Bott理论的各个方面，可以从平滑的流形的经典环境扩展到具有全态$ \ MATHBB {C}^*$ ACTION的复杂分析空间。我们扩展了有关Bialynicki-birula分解的先前结果，用于紧凑，复杂的Kähler歧管将其扩展到非紧密复杂的复杂歧管，并开发Bialynicki-birula分解的功能性能，尤其是沿$ \ Mathbb {C}^*$ novariant to Blowup沿爆炸而言。我们推断出$ \ mathbb {c}^*$ - 不变，封闭，复杂的复杂分析子空间的复杂分析的复杂分解的bialynicki-birula分解的存在；在固定点上产生几何后果，以造成双林基 - 双鲁拉无效，共同索引和索引的阳性；我们通过将奇点的分辨率应用于分析空间来开发这些结果的更强版本。
Our goal in this work is to develop aspects of Bialynicki-Birula and Morse-Bott theory that can be extended from the classical setting of smooth manifolds to that of complex analytic spaces with a holomorphic $\mathbb{C}^*$ action. We extend prior results on existence of Bialynicki-Birula decompositions for compact, complex Kähler manifolds to non-compact complex manifolds and develop functorial properties of the Bialynicki-Birula decomposition, in particular with respect to blowup along a $\mathbb{C}^*$-invariant, embedded complex submanifold. We deduce the existence of a Bialynicki-Birula decomposition for a $\mathbb{C}^*$-invariant, closed, complex analytic subspace of complex manifold with a $\mathbb{C}^*$ action; derive geometric consequences for the positivity of the Bialynicki-Birula nullity, co-index, and index at a fixed point; and we develop stronger versions of these results by applying resolution of singularities for analytic spaces.
