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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1194345
Page Count: 10
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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.
Proceedings of the American Mathematical Society © 2003 American Mathematical Society