Budur, Nero; Wang, Botong; Yoon, Youngho Rank one local systems and forms of degree one. (English) Zbl 1404.14013 Int. Math. Res. Not. 2016, No. 13, 3849-3855 (2016). Summary: Cohomology support loci of rank one local systems of a smooth quasi-projective complex algebraic variety are finite unions of torsion-translated complex subtori of the character variety of the fundamental group. Tangent spaces of the character variety are (partially) represented by logarithmic 1-forms. In this paper, we give a relation between cohomology support loci and the natural strata of 1-forms given by the dimension of the vanishing locus. This relation generalizes the one for the projective case due to Green and Lazarsfeld and also generalizes the partial relation due to Dimca in the quasi-projective case. Cited in 1 Document MSC: 14C20 Divisors, linear systems, invertible sheaves 14C30 Transcendental methods, Hodge theory (algebro-geometric aspects) 14F40 de Rham cohomology and algebraic geometry PDFBibTeX XMLCite \textit{N. Budur} et al., Int. Math. Res. Not. 2016, No. 13, 3849--3855 (2016; Zbl 1404.14013) Full Text: DOI arXiv