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arXiv · 2506.23124

Arithmetic non-very generic arrangements

Pragnya Das·Takuya Saito·Simona Settepanella
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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.

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Pragnya Das, Takuya Saito, Simona Settepanella. 2025-06-29. Arithmetic non-very generic arrangements. https://doi.org/10.1007/s10801-026-01509-8

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