Tropical polytopes and cellular resolutions

Details Tropical polytopes and cellular resolutions Tropical polytopes and cellular resolutions

2006-05-18

arxiv.org/abs/math/0605494v2

Experimental Mathematics 16 (2007), no. 3, 277--291

Mathematics

Combinatorics

19 pages, 13 figures

Scientific paper

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 which 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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