Mathematics – Algebraic Geometry
Scientific paper
2000-10-11
Contemporary Math., Amer. Math. Soc., vol. 276 (2001), pp. 43-79
Mathematics
Algebraic Geometry
Revised and expanded; 37 pages, 13 figures; to appear in Contemporary Mathematics (Proceedings of the AMS Special Session ``En
Scientific paper
This is a survey of some recent developments in the study of complements of line arrangements in the complex plane. We investigate the fundamental groups and finite covers of those complements, focusing on homological and enumerative aspects. The unifying framework for this study is the stratification of the character variety of the fundamental group, G, by the jumping loci for cohomology with coefficients in rank 1 local systems. Counting certain torsion points on these "characteristic" varieties yields information about the homology of branched and unbranched covers of the complement, as well as on the number of low-index subgroups of its fundamental group. We conclude with two conjectures, expressing the lower central series quotients of G/G'' (and, in some cases, G itself) in terms of the closely related "resonance" varieties. We illustrate the discussion with a number of detailed examples, some of which reveal new phenomena.
Suciu Alexander I.
No associations
LandOfFree
Fundamental groups of line arrangements: Enumerative aspects does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Fundamental groups of line arrangements: Enumerative aspects, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fundamental groups of line arrangements: Enumerative aspects will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-407054