发表机构
ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在统一框架下，以积分横截性为关键工具，将多面体的取面、取切片、相交等构造对应到辛环面流形侧的几何构造，确保构造的幺模性与光滑性。
AI 中文摘要
在Delzant理论框架中，辛环面流形对应幺模多面体，而保幺模性的多面体构造对应流形侧的几何构造。我们在统一框架下处理取面、取切片、多面体相交等构造，将其分别对应流形侧的不变子流形、辛约化、乘积约化（完整列表见表1）。关键工具是“积分横截性”，这是一种格细化的横截条件，为保幺模性提供了统一判据，确保流形侧的光滑性。为将所有构造限定在单个环境向量空间（固定环面李代数的对偶空间）内，我们允许所涉及的环面作用具有非平凡但连通的核。
英文摘要
In the Delzant world, symplectic toric manifolds correspond to unimodular polytopes, and unimodularity-preserving polytope constructions correspond to geometric constructions on the manifold side. We treat, in a unified framework, constructions such as taking a face, taking a slice, and polytope intersections, identifying each with its geometric counterpart, namely invariant submanifolds, symplectic reduction, and reduction of a product (a full list appears in Table 1). The key tool is "integral transversality", a lattice-refined transversality condition that provides a uniform criterion for preserving unimodularity, ensuring smoothness on the manifold side. To keep every construction within a single ambient vector space -- the dual of the Lie algebra of a fixed torus -- we allow the torus actions involved to have nontrivial, but connected kernels.
Comments54 pages, 5 figures
