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Rational versus real cohomology algebras of low-dimensional toric varieties

Author: Eva Maria Feichtner
Journal: Proc. Amer. Math. Soc. 131 (2003), 1695-1704
MSC (2000): Primary 14M25; Secondary 14F25, 52B20
Published electronically: October 1, 2002
MathSciNet review: 1955255
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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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Additional Information

Eva Maria Feichtner
Affiliation: Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland

Keywords: Toric varieties, cohomology algebras, simplicial fans, Hodge-Riemann-Minkowski inequalities
Received by editor(s): May 14, 1999
Received by editor(s) in revised form: December 18, 2001, January 25, 2002, and January 30, 2002
Published electronically: October 1, 2002
Communicated by: John R. Stembridge
Article copyright: © Copyright 2002 American Mathematical Society