发表机构
University of Toronto（多伦多大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究哈密顿环面作用的动量多胞体，证明其典范仿射分层的各层恰为腔室面的相对内部，并补充了这些面构成多面体复形的缺失证明，同时将结果推广至正常映射情形及紧致 Kähler 情形。
AI 中文摘要
对于紧致连通的哈密顿 $T$-空间（其中 $T$ 为环面），动量映射的（相对）正则值集合的分支是开凸多胞体，其闭包（称为腔室）构成动量多胞体的多面体分解。在之前的一篇论文中，我们证明了动量多胞体存在一个典范的仿射分层，该分层具有如下性质：当在某一层中变化时，动量映射的纤维作为 $T$-空间不发生变化。在本文中，我们证明该分层的各层正是腔室的面的相对内部。在此过程中，我们还给出了这些面构成一个多面体复形的证明，该事实（似乎）在文献中缺失。我们进一步将上述结果推广到动量映射作为到凸集的映射是正常映射的哈密顿 $T$-空间，并且在紧致 Kähler 情形下，我们指出了上述各层可以用 $T_\mathbb{C}$-轨道闭包多胞体来描述。
英文摘要
For a compact connected Hamiltonian $T$-space (with $T$ a torus), the components of the set of (relative) regular values of the momentum map are open convex polytopes, whose closures (called the chambers) form a polyhedral decomposition of the momentum polytope. In a previous paper we showed that there is a canonical affine stratification of the momentum polytope with the property that, while varying through a stratum, the fibers of the momentum map do not change as $T$-spaces. In this paper we show that the strata of this stratification are the relative interiors of the faces of the chambers. In doing so, we also give a proof of the fact that these faces form a polyhedral complex, which (it seems) was missing from the literature. We further extend the above to Hamiltonian $T$-spaces whose momentum map is proper as map into a convex set and, in the compact Kähler case, we point out a description of the above strata in terms of the $T_\mathbb{C}$-orbit closure polytopes.
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