The rational homology of toric varieties is not a combinatorial invariant

Mark McConnell

doi:10.1090/S0002-9939-1989-0954374-9

The rational homology of toric varieties is not a combinatorial invariant

Mark McConnell

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12 Scopus citations

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 language	English (US)
Pages (from-to)	986-991
Number of pages	6
Journal	Proceedings of the American Mathematical Society
Volume	105
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-1989-0954374-9
State	Published - Apr 1989
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

F-vector
Polytopes
Toric varieties

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10.1090/S0002-9939-1989-0954374-9

Cite this

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AB - 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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KW - Toric varieties

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The rational homology of toric varieties is not a combinatorial invariant

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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