The Tropical Grassmannian

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dc.creatorSpeyer, David
dc.creatorSturmfels, Bernd
dc.date2003-04-16
dc.date2003-10-17
dc.date.accessioned2026-07-07T04:56:57Z
dc.date.available2026-07-07T04:56:57Z
dc.descriptionIn tropical algebraic geometry, the solution sets of polynomial equations are piecewise-linear. We introduce the tropical variety of a polynomial ideal, and we identify it with a polyhedral subcomplex of the Grobner fan. The tropical Grassmannian arises in this manner from the ideal of quadratic Plucker relations. It is shown to parametrize all tropical linear spaces. Lines in tropical projective space are trees, and their tropical Grassmannian G_{2,n} equals the space of phylogenetic trees studied by Billera, Holmes and Vogtmann. Higher Grassmannians offer a natural generalization of the space of trees. Their facets correspond to binomial initial ideals of the Plucker ideal. The tropical Grassmannian G_{3,6} is a simplicial complex glued from 1035 tetrahedra.
dc.descriptionCorrected small errors, added new section on characteristic independence
dc.identifierhttps://arxiv.org/abs/math/0304218
dc.identifierhttp://arxiv.org/abs/math/0304218
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67104
dc.subjectAlgebraic Geometry
dc.subjectCombinatorics
dc.titleThe Tropical Grassmannian
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