Tropical Polytopes and Cellular Resolutions

@article{Develin2007TropicalPA,
  title={Tropical Polytopes and Cellular Resolutions},
  author={Mike Develin and Josephine Yu},
  journal={Experimental Mathematics},
  year={2007},
  volume={16},
  pages={277 - 291}
}
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 [Bayer and Sturmfels 98], 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… 
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