Geometric structures on the complement of a projective arrangement
| dc.creator | Couwenberg, Wim | |
| dc.creator | Heckman, Gert | |
| dc.creator | Looijenga, Eduard | |
| dc.date | 2003-11-24 | |
| dc.date | 2004-04-27 | |
| dc.date.accessioned | 2026-07-07T05:03:11Z | |
| dc.date.available | 2026-07-07T05:03:11Z | |
| dc.description | 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. | |
| dc.description | 70 pages, v2: We give a better (sharper) formulation of the main result and added some references | |
| dc.identifier | https://arxiv.org/abs/math/0311404 | |
| dc.identifier | http://arxiv.org/abs/math/0311404 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69313 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.subject | 33C67, 33D80 | |
| dc.title | Geometric structures on the complement of a projective arrangement | |
| dc.type | text |