AI 中文总结
本文提出名为万花筒（kaleidoscope）的多面体模型，通过矩多面体组合学研究环面实轨迹拓扑，给出可定向性判据与欧拉示性数公式，统计复维数≤9的光滑环面法诺簇中实轨迹可定向的数量。
AI 中文摘要
环面实轨迹是环面对称辛流形中特殊的拉格朗日子流形。我们基于矩映射的限制，开发了环面实轨迹的多面体模型，称为万花筒（kaleidoscope）。该构造为环面实轨迹的拓扑提供了直接的几何描述，给出了可定向性的简单判据和欧拉示性数的清晰公式。我们用大量例子阐释该理论，并对复维数不超过9的所有光滑环面法诺簇，统计其实轨迹可定向的数量。万花筒构造提供了一种简单、直观且有效的框架，可通过矩多面体的组合学理解环面实轨迹的拓扑。
英文摘要
Toric real loci are distinguished lagrangian submanifolds of toric symplectic manifolds. We develop a polyhedral model for toric real loci, called a kaleidoscope, based on the restriction of the moment map. This construction provides a direct geometric description of the topology of toric real loci and leads to simple criteria for orientability, together with transparent formulas for the Euler characteristic. We illustrate the theory with numerous examples and count, in every complex dimension up to 9, the smooth toric Fano varieties whose real loci are orientable. The kaleidoscope construction offers a simple, visual, and effective framework for understanding the topology of toric real loci through the combinatorics of their moment polytopes.
Comments49 pages, 16 figures
