Tropical Ideals and Discriminants
Kayleigh L Ward · 2020
Tropical ideals arose in the work of Maclagan-Rincon and Giansiracusa-Giansiracusa in the context of their scheme-theoretic refinement of tropicalization. An open problem is to understand what geometric information about a variety V (I) is encoded in the tropical ideal trop(I). In this thesis we focus on the valuation of the discriminant for certain classes of projective hypersurfaces of low-degree in both characteristic 0 and p. We find both cases where the valuation of the discriminant is determined by trop(I), and cases where it is not.