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- Title
Characteristic varieties and logarithmic differential 1-forms.
- Authors
Dimca, Alexandru
- 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.
- Subjects
HOMOLOGY theory; LOGARITHMIC functions; ELLIPTIC curves; ALGEBRA; ISOMORPHISM (Mathematics)
- Publication
Compositio Mathematica, 2010, Vol 146, Issue 1, p129
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X09004461