A counterexample to the maximality of toric varieties

Hower, Valerie

doi:10.1090/S0002-9939-08-09431-8

A counterexample to the maximality of toric varieties
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Proc. Amer. Math. Soc. 136 (2008), 4139-4142 Request permission

Abstract:

We present a counterexample to the conjecture of Bihan, Franz, McCrory, and van Hamel concerning the maximality of toric varieties. There exists a six dimensional projective toric variety $X$ with the sum of the $\mathbb {Z}_2$ Betti numbers of $X(\mathbb {R})$ strictly less than the sum of the $\mathbb {Z}_2$ Betti numbers of $X(\mathbb {C})$.

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