Volume polynomials and duality algebras of multi-fans

DOI10.1007/s40598-016-0048-4zbMath1432.52021arXiv1509.03008OpenAlexW3104530247MaRDI QIDQ338647

Mikiya Masuda, Anton A. Ayzenberg

Publication date: 7 November 2016

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.03008

zbMATH Keywords

Stanley-Reisner ringMacaulay dualityMinkowski relationsMinkowski theoremmulti-fanmulti-polytopePoincare duality algebratorus manifoldvolume polynomial

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) (n)-dimensional polytopes (52B11) Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.) (52B40) Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35) Mixed volumes and related topics in convex geometry (52A39) Algebraic topology of manifolds (57N65) Polyhedral manifolds (52B70) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40)

Related Items

Dimensions of multi-fan duality algebras, Quasitoric totally normally split manifolds, The volume polynomial of regular semisimple Hessenberg varieties and the Gelfand-Zetlin polytope, Manifolds of isospectral arrow matrices, Generalized virtual polytopes and quasitoric manifolds

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