Valuated term orders are studied for the purposes of Gröbner theory over fields with valuation. The points of a usual tropical variety correspond to certain valuated terms preorders. Generalizing both of these, the set of all ``well-behaved'' valuated term preorders is canonically in bijection with the points of a space introduced in our previous work on tropical adic geometry. In this paper we interpret these points geometrically by explicitly characterizing them in terms of classical polyhedral geometry. This characterization gives a bijection with equivalence classes of flags of polyhedra which also classifies valuated term orders.
Geometric interpretation of valuated term (pre)orders
Kalina Mincheva, Tulane UniversityAuthors: Netanel Friedenberg, Kalina Mincheva
2023 AWM Research Symposium
Tropical Geometry [Organized by Josephine Yu and Abeer Al Ahmadieh]