Hard Lefschetz theorem and Hodge-Riemann relations for intersection cohomology of nonrational polytopes

DOI10.1512/iumj.2005.54.2528zbMath1171.14034arXivmath/0302236OpenAlexW2091984925MaRDI QIDQ4682095

Valery A. Lunts, Paul Bressler

Publication date: 9 June 2005

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0302236

zbMATH Keywords

toric varietiesintersection cohomologyalgebraic geometryconvex geometry

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Intersection homology and cohomology in algebraic topology (55N33)

Related Items (11)

The hypertoric intersection cohomology ring ⋮ Convex polytopes and quasilattices from the symplectic viewpoint ⋮ Nonpolytopal nonsimplicial lattice spheres with nonnegative toric \(g\)-vector ⋮ The work of June Huh ⋮ On the anisotropy theorem of Papadakis and Petrotou ⋮ Relative Hard Lefschetz theorem for fans ⋮ Quantum (non-commutative) toric geometry: foundations ⋮ Recent developments in algebraic combinatorics ⋮ The decomposition theorem, perverse sheaves and the topology of algebraic maps ⋮ Filtrations on combinatorial intersection cohomology and invariants of subdivisions ⋮ Combinatorial duality and intersection product: a direct approach

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