2008/05/31 by Alexandru Dimca · 7 citations
Mathematics · #Algebraic Geometry and Number Theory #Ambient space #Codimension #Commutative Algebra and Its Applications #Compactification (mathematics) #Differential (mechanical device) #Differential geometry #Geometry and complex manifolds #Logarithm #Rank (graph theory) #Variety (cybernetics) #math.AG #math.AT #msc:14C30 #msc:14F40 #msc:14H52 #msc:32S22
paper · pdf · doi:10.1112/s0010437x09004461
published in Compositio Mathematica 146(1), 129-144 (Cambridge University Press) · 18 pages, in this new version Remark 6.4 is extended, a reference to a result by Green and Lazarsfeld is added and some minor corrections are done
arxiv created 2008/11/13 · openalex publication_date 2010/01/01 · openalex created_date 2016/06/24 · arxiv updated 2019/02/20 · openalex updated_date 2026/08/05
Abstract We introduce in this paper a hypercohomology version of the resonance varieties and obtain some relations to the characteristic varieties of rank one local systems on a smooth quasi-projective complex variety M . A logarithmic resonance variety is also considered and, as an application, we determine the first characteristic variety of the configuration space of n distinct labeled points on an elliptic curve. Finally, for a logarithmic 1-form α on M we investigate the relation between the resonance degree of α and the codimension of the zero set of α on a good compactification of M . This question was inspired by the recent work by Cohen, Denham, Falk and Varchenko.