Anastasia Nathanson, University of Minnesota
Authors: Anastasia Nathanson, Dustin Ross
2023 AWM Research Symposium
Tropical Geometry [Organized by Josephine Yu and Abeer Al Ahmadieh]

Associated to any divisor in the Chow ring of a simplicial tropical fan, we discuss the construction of a family of polytopal complexes, called normal complexes, which we propose as an analogue of the well-studied notion of normal polytopes from the setting of complete fans. The talk will describe certain closed convex polyhedral cones of divisors for which the “volume” of each divisor in the cone—that is, the degree of its top power—is equal to the volume of the associated normal complexes. One can view the theory of normal complexes developed in the talk as a polytopal model underlying the combinatorial Hodge theory pioneered by Adiprasito, Huh, and Katz.

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