Exponential actions defined by vector configurations, Gale duality, and moment-angle manifolds

Abstract

Exponential actions defined by vector configurations provide a universal framework for several constructions of holomorphic dynamics, non-Kaehler complex geometry, toric geometry and topology. These include leaf spaces of holomorphic foliations, intersections of real and Hermitian quadrics, the quotient construction of simplicial toric varieties, LVM and LVMB manifolds, complex-analytic structures on moment-angle manifolds and their partial quotients. In all of these cases, the geometry and topology of the appropriate quotient object can be described by combinatorial data including a pair of Gale dual vector configurations.

52 pages, published version

References in corpus (11)

• Foliations modeling nonrational simplicial toric varieties
• Complex geometry of moment-angle manifolds
• Operations on polyhedral products and a new topological construction of infinite families of toric manifolds
• Generalized toric varieties for simple non-rational convex polytopes
• Complex-analytic structures on moment-angle manifolds
• LVMB manifolds and quotients of toric varieties
• Torus actions, combinatorial topology and homological algebra
• Nonrational polytopes and fans in toric geometry
• Transverse Kähler structures on central foliations of complex manifolds
• Norm minima in certain Siegel leaves
• Dolbeault cohomology of complex manifolds with torus action