回归共线点空间是可壳的
The space of tropically collinear points is shellable
摘要：
在一个固定的热带射影空间TP^{d-1}中n个热带共线点的空间T_{d,n}等价于秩不超过2的矩阵的行列式簇的热带化，它由热带秩或Kapranov秩不超过2的实d × n矩阵组成，模列的射影等价。我们证明了它等于在评价映射下TP^{d-1}中n个标记热带线的模空间M_{0,n}（TP^{d-1}，1）的像。因此，我们利用M_{0,n}（TP^{d-1}，1）的单纯扇形结构导出了T_{d,n}的自然单纯扇形结构，它与d+n类群系统发育树空间的单纯扇形结构一致. Trappmann和Ziegler已经证明系统发育树的空间是可壳的。使用类似的方法，我们证明了T_{d,n}是壳与我们的单纯扇结构和计算同源的链接的起源。T_{d,n}的可壳性已在2005年由Aluminin证实。
英文摘要：
The space T_{d,n} of n tropically collinear points in a fixed tropical projective space TP^{d-1} is equivalent to the tropicalization of the determinantal variety of matrices of rank at most 2, which consists of real d x n matrices of tropical or Kapranov rank at most 2, modulo projective equivalence of columns. We show that it is equal to the image of the moduli space M_{0,n}(TP^{d-1},1) of n-marked tropical lines in TP^{d-1} under the evaluation map. Thus we derive a natural simplicial fan structure for T_{d,n} using a simplicial fan structure of M_{0,n}(TP^{d-1},1) which coincides with that of the space of phylogenetic trees on d+n taxa. The space of phylogenetic trees has been shown to be shellable by Trappmann and Ziegler. Using a similar method, we show that T_{d,n} is shellable with our simplicial fan structure and compute the homology of the link of the origin. The shellability of T_{d,n} has been conjectured by Develin in 2005.
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