Rational versus real cohomology algebras of low-dimensional toric varieties

Feichtner, Eva

doi:10.1090/S0002-9939-02-06735-7

Rational versus real cohomology algebras of low-dimensional toric varieties
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by Eva Maria Feichtner PDF

Proc. Amer. Math. Soc. 131 (2003), 1695-1704 Request permission

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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