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Rational versus Real Cohomology Algebras of Low-Dimensional Toric Varieties

Eva Maria Feichtner
Proceedings of the American Mathematical Society
Vol. 131, No. 6 (Jun., 2003), pp. 1695-1704
Stable URL: http://www.jstor.org/stable/1194345
Page Count: 10
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Rational versus Real Cohomology Algebras of Low-Dimensional Toric Varieties
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Abstract

We show that the real cohomology algebra of a compact toric variety of complex dimension 2 is determined, up to isomorphism, by the combinatorial data of its defining fan. Surprisingly enough, this is no longer the case when taking rational coefficients. Moreover, we show that neither the rational nor the real or complex cohomology algebras of compact quasi-smooth toric varieties are combinatorial invariants in general.

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