Tropical Polytopes and Cellular Resolutions
Tropical Polytopes and Cellular Resolutions
复制标题
热带多面体和细胞分辨率
DOI：
10.1080/10586458.2007.10129009
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发表时间：
2006
影响因子：
0.5
通讯作者：
Josephine Yu
中科院分区：
文献类型：
--
作者：
M. Develin;Josephine Yu
热带多面体是多面体在度映射下的Puietrix级数域上的仿射空间中的图像。这种观点产生了一族单项式理想的胞元分解，它们推广了Bayer和Sturmfels的船体复形[Bayer and Sturmfels 98]，其实例在更小的意义上改进了船体分解。我们还提出了一个新的定义的一个面的热带多面体，它有更好的性能比以前的定义，我们给出的例子，并提供了许多的结构和方向，在这方面的进一步研究。
Tropical polytopes are images of polytopes in an affine space over the Puiseux series field under the degree map. This viewpoint gives rise to a family of cellular resolutions of monomial ideals that generalize the hull complex of Bayer and Sturmfels [Bayer and Sturmfels 98], instances of which improve upon the hull resolution in the sense of being smaller. We also suggest a new definition of a face of a tropical polytope, which has nicer properties than previous definitions; we give examples and provide many conjectures and directions for further research in this area.