Mathematics – Algebraic Geometry
Scientific paper
2003-11-24
Mathematics
Algebraic Geometry
70 pages, v2: We give a better (sharper) formulation of the main result and added some references
Scientific paper
Consider a complex projective space with its Fubini-Study metric. We study certain one parameter deformations of this metric on the complement of an arrangement (=a finite union of hyperplanes) whose Levi-Civita connection is of Dunkl type--interesting examples are obtained from the arrangements defined by finite complex reflection groups. We determine a parameter interval for which the metric is locally of Fubini-Study type, flat, or complex-hyperbolic. We find a finite subset of this interval for which we get a complete orbifold or at least a Zariski open subset thereof, and we analyze these cases in some detail (e.g., we determine their orbifold fundamental group). In this set-up, the principal results of Deligne-Mostow on the Lauricella hypergeometric differential equation and work of Barthel-Hirzebruch-Hoefer on arrangements in a projective plane appear as special cases. Along the way we produce in a geometric manner all the pairs of complex reflection groups with isomorphic discriminants, thus providing a uniform approach to work of Orlik-Solomon.
Couwenberg Wim
Heckman Gert
Looijenga Eduard
No associations
LandOfFree
Geometric structures on the complement of a projective arrangement 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 Geometric structures on the complement of a projective arrangement, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Geometric structures on the complement of a projective arrangement will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-20090