Hard Lefschetz theorem for nonrational polytopes

@inproceedings{Karu2001HardLT,
  title={Hard Lefschetz theorem for nonrational polytopes},
  author={K. Karu},
  year={2001}
}
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. 
Highly Cited
This paper has 40 citations. REVIEW CITATIONS
31 Citations
15 References
Similar Papers

References

Publications referenced by this paper.
Showing 1-10 of 15 references

Combinatorial Intersection cohomology for Fans

  • G. Barthel, J.-P. Brasselet, K.-H. Fieseler, L. Kaup
  • Tôhoku Math. J. 54,
  • 2002
Highly Influential
10 Excerpts

On Simple Polytopes

  • P. McMullen
  • Invent. math. 113,
  • 1993
Highly Influential
7 Excerpts

The number of faces of a simplicial convex polytope

  • R. Stanley
  • Adv. Math
  • 1980
Highly Influential
6 Excerpts

An analogue of the Hodge-Riemann relations for simple convex polytopes

  • V. Timorin
  • Russian Math. Surveys
  • 1999
Highly Influential
4 Excerpts

On polytopes simple in edges . ( Russian ) Funkts

  • V. Timorin
  • Anal . Prilozh .
  • 2001

On polytopes simple in edges, (Russian) Funktsional

  • V. Timorin
  • Anal. i Prilozhen
  • 2001
2 Excerpts

The Structure of the Polytope

  • M. Brion
  • Algebra, Tôhoku Math. J
  • 1997
1 Excerpt

The Structure of the Polytope Algebra

  • M. Brion
  • Tôhoku Math . J .
  • 1997

Rational Intersection Cohomology of Projective Toric Varieties

  • K.-H. Fieseler
  • Journal f.d. reine u. angew. Mathematik
  • 1991
1 Excerpt

Similar Papers

Loading similar papers…