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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The rational homology of toric varieties is not a combinatorial invariant


Author: Mark McConnell
Journal: Proc. Amer. Math. Soc. 105 (1989), 986-991
MSC: Primary 14L32; Secondary 14F45, 14J40, 52A25, 52A37
MathSciNet review: 954374
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1989-0954374-9
PII: S 0002-9939(1989)0954374-9
Keywords: Polytopes, toric varieties, $ f$-vector
Article copyright: © Copyright 1989 American Mathematical Society