FAQ on the g-theorem and the hard Lefschetz theorem for face rings

zbMath1443.05189arXiv1906.05859MaRDI QIDQ5108274

Karim A. Adiprasito

Publication date: 30 April 2020

Full work available at URL: https://arxiv.org/abs/1906.05859

zbMATH Keywords

hard Lefschetz theoremface rings

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Triangulating manifolds (57Q15) Polyhedral manifolds (52B70) Topological aspects of complex singularities: Lefschetz theorems, topological classification, invariants (32S50) Combinatorial aspects of simplicial complexes (05E45) Combinatorial aspects of commutative algebra (05E40)

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Cites Work

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• Hard Lefschetz theorem for simple polytopes
• The canonical module of a Stanley-Reisner ring
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• The number of faces of a simplicial convex polytope
• Torus embeddings and dualizing complexes
• Unshellable triangulations of spheres
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• Combinatorics and commutative algebra.
• P.L.-spheres, convex polytopes, and stress
• Lefschetz properties and basic constructions on simplicial spheres
• Toric chordality
• The numbers of faces of simplicial polytopes

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