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Geometric structures on the complement of a projective arrangement

Wim Couwenberg, Gert Heckman, Eduard Looijenga (2005)

Publications Mathématiques de l'IHÉS

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 (= 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...

Global Parametrization of Scalar Holomorphic Coadjoint Orbits of a Quasi-Hermitian Lie Group

Benjamin Cahen (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Let G be a quasi-Hermitian Lie group with Lie algebra 𝔤 and K be a compactly embedded subgroup of G . Let ξ 0 be a regular element of 𝔤 * which is fixed by K . We give an explicit G -equivariant diffeomorphism from a complex domain onto the coadjoint orbit 𝒪 ( ξ 0 ) of ξ 0 . This generalizes a result of [B. Cahen, Berezin quantization and holomorphic representations, Rend. Sem. Mat. Univ. Padova, to appear] concerning the case where 𝒪 ( ξ 0 ) is associated with a unitary irreducible representation of G which is holomorphically...

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