The rational homology of toric varieties is not a combinatorial invariant

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Abstract

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
Volume105
Issue number4
DOIs
StatePublished - Apr 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • F-vector
  • Polytopes
  • Toric varieties

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