Characteristic Varieties for a Class of Line Arrangements

Abstract

Abstract. Let A be a line arrangement in the complex projective plane P 2 , having the points of multiplicity ≥ 3 situated on two lines in A, say H 0 and H∞. Then we show that the non-local irreducible components of the first resonance variety R 1 (A) are 2-dimensional and correspond to parallelograms P in C 2 = P 2 \ H∞ whose sides are in A and for which H 0 is a diagonal.

On the Monodromy of Milnor Fibers of Hyperplane Arrangements

“…With the description of the irreductible components of the first resonance variety for a C 2 arrangement, (see Theorem 4.3 of [9]) we have a contradiction with the fact that ω H = 0 ∀H. Hence H 1 (H * (M(A ′ ), C), ω∧) = 0, and we have that…”

Admissibility of Local Systems for some Classes of Line Arrangements

“…If all points of multiplicity ≥ 3 are situated on a line, the arrangement is a nodal affine arrangement; see [3,8]. Theorem 1.2 above shows that for such arrangements, which are said to be of type C 1 , all rank one local systems on their complements are admissible.…”