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2007 Tropical Polytopes and Cellular Resolutions
Mike Develin, Josephine Yu
Experiment. Math. 16(3): 277-292 (2007).


Tropical polytopes are images of polytopes in an affine space over the Puiseux series field under the degree map. This viewpoint gives rise to a family of cellular resolutions of monomial ideals that generalize the hull complex of Bayer and Sturmfels, instances of which improve upon the hull resolution in the sense of being smaller. We also suggest a new definition of a face of a tropical polytope, which has nicer properties than previous definitions; we give examples and provide many conjectures and directions for further research in this area.


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Mike Develin. Josephine Yu. "Tropical Polytopes and Cellular Resolutions." Experiment. Math. 16 (3) 277 - 292, 2007.


Published: 2007
First available in Project Euclid: 7 March 2008

zbMATH: 1134.52006
MathSciNet: MR2367318

Primary: 13D02 , 52A30

Keywords: cellular resolution , monomial ideal , Tropical polytope

Rights: Copyright © 2007 A K Peters, Ltd.

Vol.16 • No. 3 • 2007
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