2023/01/06 by Bossinger, Lara · 2 citations
#13P10 #14M25 (Primary) #14T05 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2301.02545
In this survey I summarize the constructions of toric degenerations obtained from valuations and Gröbner theory and describe in which sense they are equivalent. I show how adapted bases can be used to generalize the classical Newton polytope to what is called a \mathbb B-Newton polytope. The \mathbb B-Newton polytope determines the Newton--Okounkov polytopes of all Khovanskii-finite valuations sharing the adapted standard monomial basis \mathbb B.