2016/12/15 by Tripoli, Paolo
#14T05 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.1612.05192
Given a projective variety X of codimension k+1 in ℙn the Chow hypersurface ZX is the hypersurface of the Grassmannian Gr(k, n) parametrizing projective linear spaces that intersect X. We introduce the tropical Chow hypersurface Trop(ZX). This object only depends on the tropical variety Trop(X) and we provide an explicit way to obtain Trop(ZX) from Trop(X). We also give a geometric description of Trop(ZX). We conjecture that, as in the classical case, Trop(X) can be reconstructed from Trop(ZX) and prove it for the case when X is a curve in ℙ3. This suggests that the tropical Chow hypersurface can be used to construct a tropical Chow variety.