ARITHMETIC NON-VERY GENERIC ARRANGEMENTS

A discriminantal hyperplane arrangement B(n, k, A) is constructed from a given generic hyperplane arrangement A. The arrangement A is classified as either very generic or non-very generic according to the combinatorial structure of B(n, k, A). In particular, A is regarded as non-very generic if the intersection lattice of B(n, k, A) contains at least one non-very generic intersection, namely, an intersection that does not satisfy a specific rank condition established by Athanasiadis. In this paper, we present arithmetic criteria characterizing non-very generic intersections in discriminantal arrangements, and we complete and correct a previous result of Libgober and the third author concerning rank 2 intersections in such arrangements.