Josephine Yu, Massachusetts Institute of Technology
The space of tropically collinear points are shellable

The space T_d,n of n tropically collinear points in a fixed tropical projective space TP^d-1 is the tropicalization of the determinantal variety of matrices of rank 2. It consists of real d x n matrices of tropical or Kapranov rank 2. We show that it is equal to the image of the moduli of n-marked tropical lines in TP^d-1 under the evaluation map. Thus we derive a natural simplicial complex 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. Here we show that T_d,n is shellable with our simplicial complex structure, prove. We also compute its homology. This is joint work with Hannah Markwig.

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