2018/04/05 by Georgy Scholten, Cynthia Vinzant, Scholten, Georgy +1
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1804.02029
openalex publication_date 2018/04/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The image of a linear space under inversion of some coordinates is an affine\nvariety whose structure is governed by an underlying hyperplane arrangement. In\nthis paper, we generalize work by Proudfoot and Speyer to show that circuit\npolynomials form a universal Groebner basis for the ideal of polynomials\nvanishing on this variety. The proof relies on degenerations to the\nStanley-Reisner ideal of a simplicial complex determined by the underlying\nmatroid. If the linear space is real, then the semi-inverted linear space is\nalso an example of a hyperbolic variety, meaning that all of its intersection\npoints with a large family of linear spaces are real.\n