A geometric perspective on plus-one generated arrangements of lines (Q6597297)

The authors consider some special types of arrangements of lines and study the relationship between them: free arrangements, plus-one generated projective line arrangements of given exponents, next to free arrangements, next to free minus arrangements and next to free plus arrangements. A theorem on the intersection between a line and the scheme of zeroes associated with a plus-one generated projective line arrangement is proven, retrieving some existing results and extending similar results for nearly free arrangements previously obtained by the authors. A geometric characterization of plus-one generated projective line arrangements that are either next-to-free plus or next-to-free minus is proven. Interesting examples and particular cases are discussed.