保角极限与联络空间的Bialynicki-Birula分层
Conformal limits and the Bialynicki-Birula stratification of the space of lambda-connections
摘要：
在Higgs丛的模空间上的Morse分层和在全纯联络的de Rham模空间上的部分oper分层中，对Higgs联络空间的Bialynicki-Birula分解是有限制的.对于Morse和部分操作，每一层都是Hodge结构的复变空间的一个分量上的全纯拉格朗日纤维化。本文将已知的关于Hitchin截面和算子空间的结果推广到任意地层。其中包括：通过Gaiotto的“h-棒-共形极限”对Hodge结构稳定变化上的两个层的纤维进行了双全纯识别，证明了Morse和部分opstratification的纤维在基点处是横截的，并将纤维明确参数化为半维仿射空间.
英文摘要：
The Bialynicki-Birula decomposition of the space of lambda-connections restricts to the Morse stratification on the moduli space of Higgs bundles and to the partial oper stratification on the de Rham moduli space of holomorphic connections. For both the Morse and partial oper stratifications, every stratum is a holomorphic Lagrangian fibration over a component of the space of complex variations of Hodge structure. In this paper, we generalize known results for the Hitchin section and the space of opers to arbitrary strata. These include the following: a biholomorphic identification of the fibers of the two strata over a stable variation of Hodge structure via the "h-bar-conformal limit" of Gaiotto, a proof that the fibers of the Morse and partial oper stratifications are transverse at the base point, and an explicit parametrization of the fibers as half-dimensional affine spaces.
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