Hard Lefschetz theorem for nonrational polytopes

By Kalle Karu. 2001

113 citations recorded by the source corpus.

The Hard Lefschetz theorem is known to hold for the intersection cohomology of the toric variety associated to a rational convex polytope. One can construct the intersection cohomology combinatorially from the polytope, hence it is well defined even for nonrational polytopes when there is no variety associated to it. We prove the Hard Lefschetz theorem for the intersection cohomology of a general polytope.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/284f74772b3f6312e101051c211aa988a4c23a7e

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In Algebra and Number Theory

1. Ben Elias
2. T. Panov
3. M. A. Cataldo
4. L. Migliorini
5. Geordie Williamson
6. June Huh
7. V. Buchstaber
8. M. Masuda

In Discrete Mathematics and Combinatorics

1. T. Panov
2. Geordie Williamson
3. V. Buchstaber
4. Ben Elias
5. June Huh
6. L. Migliorini
7. M. A. Cataldo
8. M. Masuda

In Geometry and Topology

1. Ben Elias
2. Geordie Williamson
3. M. A. Cataldo
4. L. Migliorini
5. T. Panov
6. June Huh
7. V. Buchstaber
8. M. Masuda

Citations in the corpus

• The Hodge theory of Soergel bimodules (2012, background): “There are many formal similarities between the theory we develop here and the theory of intersection cohomology of nonrational polytopes, which was developed to prove Stanley’s conjecture on the unimodularity of the generalized h -vector [BL03], [Kar04], [BKBF07].”
• Toric Topology (2012, result): “[211] Kalle Karu.”
• COMBINATORIAL APPLICATIONS OF THE HODGE–RIEMANN RELATIONS (2017, background): “Kalle Karu (2004).”
• The decomposition theorem, perverse sheaves and the topology of algebraic maps (2007, background): “Karu, proved in [111] that the hard Lefschetz property and the Hodge-Riemann relations hold for every, i.”