2023/12/18 by Apostolos Thoma, Thoma, Apostolos, Marius Vlădoiu +1
Computer Science · Mathematics · #13P10 #14M25 #14N05 #52B35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.2312.11653
openalex publication_date 2023/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We describe explicitly all multisets of weights whose defining projective toric varieties are self-dual. In addition, we describe a remarkable and unexpected combinatorial behaviour of the defining ideals of these varieties. The toric ideal of a self-dual projective variety is weakly robust, that means the Graver basis is the union of all minimal binomial generating sets. When, in addition, the self-dual projective variety has a non-pyramidal configuration, then the toric ideal is strongly robust, namely the Graver basis is a minimal generating set, therefore there is only one minimal binomial generating set which is also a reduced Gröbner basis with respect to every monomial order and thus, equals the universal Gröbner basis.