2005/04/23 by Benoit Bertrand, Bertrand, Benoit
Mathematics · #14P25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14P25
paper · pdf · doi:10.48550/arxiv.math/0504482
18 pages, 1 figure
arxiv created 2005/04/23 · arxiv updated 2009/12/01
A real algebraic variety is maximal (with respect to the Smith-Thom inequality) if the sum of the Betti numbers (with ℤ2 coefficients) of the real part of the variety is equal to the sum of Betti numbers of its complex part. We prove that there exist polytopes that are not Newton polytopes of any maximal hypersurface in the corresponding toric variety. On the other hand we show that for any polytope Δ there are families of hypersurfaces with the Newton polytopes (λΔ)λ∈ ℕ that are asymptotically maximal when λ tends to infinity. We also show that these results generalize to complete intersections.