Arithmetic non-very generic arrangements

2025/06/29 by Das, Pragnya, Saito, Takuya, Settepanella, Simona
#14N20 #32S22 #52C30 #52C35 #Combinatorics (math.CO) #FOS: Mathematics #G.2.1

paper · doi:10.48550/arxiv.2506.23124

Abstract

A discriminantal hyperplane arrangement B(n,k,A) is constructed from a given (generic) hyperplane arrangement A, which is classified as either very generic or non-very generic depending on the combinatorial structure of B(n,k,A). In particular, A is considered non-very generic if the intersection lattice of B(n,k,A) contains at least one non-very generic intersection -- that is, an intersection that fails to satisfy a specific rank condition established by Athanasiadis in [1]. In this paper, we present arithmetic criteria characterizing non-very generic intersections in discriminantal arrangements and we complete and correct a previous result by Libgober and the third author concerning rank-two intersections in such arrangements.

Citations

• Degeneration in discriminantal arrangements
• Non-very generic arrangements in low dimension
• Likelihood Degenerations
• On the non-very generic intersections in discriminantal arrangements
• Pappus's Theorem in Grassmannian Gr(3,Cⁿ)
• Strata of discriminantal arrangements

Related

• Non-very generic arrangements in low dimension
• On the non-very generic intersections in discriminantal arrangements
• Degeneration in discriminantal arrangements
• A linear condition for non-very generic discriminantal arrangements
• Pythagorean Hyperplane Arrangements: Combinatorics of Gain Genericity