Characteristic varieties and logarithmic differential 1forms
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 quasiprojective complex variety $M$, see Theorem (3.1) and Corollaries (3.2) and (4.2). A logarithmic resonance variety is also considered in Proposition (4.5). As an application, we determine the first characteristic variety of the configuration space of $n$ distinct labeled points on an elliptic curve, see Proposition (5.1). Finally, for a logarithmic one form $\alpha$ on $M$ we investigate the relation between the resonance degree of $\alpha$ and the codimension of the zero set of $\alpha$ on a good compactification of $M$, see Corollary (1.1). This question was inspired by the recent work by D. Cohen, G. Denham, M. Falk and A. Varchenko.
 Publication:

arXiv eprints
 Pub Date:
 May 2008
 arXiv:
 arXiv:0805.4377
 Bibcode:
 2008arXiv0805.4377D
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Algebraic Topology;
 14C30;
 14F40 (Primary);
 14H52;
 32S22 (Secondary)
 EPrint:
 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