A counterexample to the maximality of toric varieties

2006/11/29 by Valerie Hower, Hower, Valerie
Mathematics · #14M25 (Primary) 05B35 (Secondary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #math.AG #msc:05B35 #msc:14M25

paper · pdf · doi:10.48550/arxiv.math/0611925

3 pages

arxiv created 2006/11/29 · openalex publication_date 2006/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 mod 2 Betti numbers of X(R) strictly less than the sum of the mod 2 Betti numbers of X(C).

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