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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...

Jacobi-Eisenstein series of degree two over Cayley numbers.

Minking Eie (2000)

Revista Matemática Iberoamericana

We shall develop the general theory of Jacobi forms of degree two over Cayley numbers and then construct a family of Jacobi- Eisenstein series which forms the orthogonal complement of the vector space of Jacobi cusp forms of degree two over Cayley numbers. The construction is based on a group representation arising from the transformation formula of a set of theta series.

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