Volume polynomials and duality algebras of multi-fans
Volume polynomials and duality algebras of multi-fans
复制标题
多扇体积多项式和对偶代数
DOI：
10.1007/s40598-016-0048-4
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发表时间：
2016
影响因子：
--
通讯作者：
Mikiya Masuda
中科院分区：
文献类型：
--
作者：
Anton Ayzenberg;Mikiya Masuda
我们介绍了体积多项式理论和相应的对偶代数的多扇。任何完备单形多重扇都确定一个体积多项式，其值为基于的多重多面体的体积，并利用这个齐次多项式构造了一个Poincare对偶代数。我们研究的结构和性质的和应用和连接到其他学科，如麦考利对偶，Novik-Swartz理论的面环的单纯形流形，推广闵可夫斯基定理的凸多面体，上同调的环面流形，计算量，和线性关系的权力的线性形式。特别地，我们证明了g定理的类似物不适用于多多面体。
We introduce a theory of volume polynomials and corresponding duality algebras of multi-fans. Any complete simplicial multi-fandetermines a volume polynomialwhose values are the volumes of multi-polytopes based on. This homogeneous polynomial is further used to construct a Poincare duality algebra. We study the structure and properties ofandand give applications and connections to other subjects, such as Macaulay duality, Novik–Swartz theory of face rings of simplicial manifolds, generalizations of Minkowski’s theorem on convex polytopes, cohomology of torus manifolds, computations of volumes, and linear relations on the powers of linear forms. In particular, we prove that the analogue of theg-theorem does not hold for multi-polytopes.