Exponential actions defined by vector configurations, Gale duality, and moment‐angle manifolds
Copyright policy )Exponential actions defined by vector configurations, Gale duality, and moment‐angle manifolds
AbstractExponential actions defined by vector configurations provide a universal framework for several constructions of holomorphic dynamics, non‐Kähler 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, reviewed in this survey. In all cases, the geometry and topology of the appropriate quotient object can be described by combinatorial data including a pair of Gale dual vector configurations.
- National Research University Higher School of Economics Russian Federation
- Lomonosov Moscow State University Russian Federation
Complex Variables, non-Kähler complex geometry, holomorphic foliations, Dynamical Systems (math.DS), toric geometry, toric topology, 57S12, 14M25, 32J18, 32L05, 32M25, 32Q55, 37F75, 52B35, 57R19, vector configurations, holomorphic dynamics, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, FOS: Mathematics, Algebraic Topology (math.AT), survey, Dynamical aspects of holomorphic foliations and vector fields, Complex Variables (math.CV), Toric varieties, Newton polyhedra, Okounkov bodies, intersections of real and Hermitian quadrics, Toric topology, leaf spaces, partial quotients, Dynamical Systems, Compact complex \(n\)-folds, LVM and LVMB manifolds, Algebraic Topology, Holomorphic bundles and generalizations, Gale dual vector configurations, Algebraic topology on manifolds and differential topology, combinatorial data, Gale and other diagrams, moment-angle manifolds, Topological aspects of complex manifolds, exponential actions, Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes, toric varieties
Complex Variables, non-Kähler complex geometry, holomorphic foliations, Dynamical Systems (math.DS), toric geometry, toric topology, 57S12, 14M25, 32J18, 32L05, 32M25, 32Q55, 37F75, 52B35, 57R19, vector configurations, holomorphic dynamics, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, FOS: Mathematics, Algebraic Topology (math.AT), survey, Dynamical aspects of holomorphic foliations and vector fields, Complex Variables (math.CV), Toric varieties, Newton polyhedra, Okounkov bodies, intersections of real and Hermitian quadrics, Toric topology, leaf spaces, partial quotients, Dynamical Systems, Compact complex \(n\)-folds, LVM and LVMB manifolds, Algebraic Topology, Holomorphic bundles and generalizations, Gale dual vector configurations, Algebraic topology on manifolds and differential topology, combinatorial data, Gale and other diagrams, moment-angle manifolds, Topological aspects of complex manifolds, exponential actions, Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes, toric varieties
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