
TL;DR
This paper introduces the tropical Chow hypersurface, a new tropical geometric object derived from a given tropical variety, providing explicit construction methods and conjecturing its role in reconstructing the original variety.
Contribution
It defines the tropical Chow hypersurface, relates it explicitly to the tropical variety, and proves reconstruction for certain cases, advancing tropical geometry understanding.
Findings
Explicit method to obtain $ ext{Trop}(Z_X)$ from $ ext{Trop}(X)$
Geometric description of the tropical Chow hypersurface
Proof of reconstruction for curves in $ ext{P}^3$
Abstract
Given a projective variety of codimension in the Chow hypersurface is the hypersurface of the Grassmannian parametrizing projective linear spaces that intersect . We introduce the tropical Chow hypersurface . This object only depends on the tropical variety and we provide an explicit way to obtain from . We also give a geometric description of . We conjecture that, as in the classical case, can be reconstructed from and prove it for the case when is a curve in . This suggests that the tropical Chow hypersurface can be used to construct a tropical Chow variety.
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