15 research outputs found

    Geometric structures on the complement of a projective arrangement

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    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.Comment: 70 pages, v2: We give a better (sharper) formulation of the main result and added some reference

    Denial of long-term issues with agriculture on tropical peatlands will have devastating consequences

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    A simple proof of the modular identity for theta functions

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    Contains fulltext : 19033_simpproft.pdf ( ) (Open Access)3 p

    Geometric Structures on the Complement of a Projective Arrangement

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    SPL migration tensions: an industry experience

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    In a software development environment where legacy software systems have been successfully deployed, there are tensions that deter the organization from moving towards software product line engineering (SPLE). An example is the effort required to develop a product line architecture versus time-to-market pressure or the lack of evidence to justify the benefits of SPLE. In this experience report we discuss the tensions that exist in Oce Technologies. We report that a reactive software reuse approach has not yielded the desired long-term benefits of reusability. A proactive approach requires knowledge exchange and coordination between software management and technical staff. We describe how such knowledge sharing can ease the tensions and facilitate a SPLE migration process
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