First order deformations for rank one local systemswith non vanishing cohomology
by
Anatoly Libgober
Univ. of Illinois at Chicago.

We describe a tangent cone to the variety of rank one local systems on a finite CW-complex having the dimension of k-dimensional cohomology exceeding m. This cone is identified with the space of certain complexes of abelian groups with differential induced by the cup product. In the case when the CW-complex is a quasiprojective complex algebraic variety the space of such complexes is a union of linear spaces. In particular, for an arrangement of hyperplanes, the set of 1-forms such that the corresponding Aomoto complex has k-dimensional betti number exceeding m is a union of linear space.

http://math.uic.edu/~libgober

Date received: June 3, 1999