The rational homology of toric varieties is not a combinatorial invariant

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We prove that the rational homology Betti numbers of a toric variety with singularities are not necessarily determined by the combinatorial type of the fan which defines it; that is, the homology is not determined by the partially ordered set formed by the cones in the fan. We apply this result to the study of convex polytopes, giving examples of two combinatorially equivalent polytopes for which the associated toric varieties have different Betti numbers.

Original languageEnglish (US)
Pages (from-to)986-991
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - Apr 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • F-vector
  • Polytopes
  • Toric varieties


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