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The Rational Homology of Toric Varieties is Not a Combinatorial Invariant

Mark McConnell
Proceedings of the American Mathematical Society
Vol. 105, No. 4 (Apr., 1989), pp. 986-991
DOI: 10.2307/2047063
Stable URL: http://www.jstor.org/stable/2047063
Page Count: 6
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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.

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