2014/09/05 by David Schmitz, Schmitz, David, Henrik Seppänen +1
Mathematics · #14C20 #14L30 #20G5 #Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT #msc:14C20 #msc:14L30 #msc:20G5
paper · pdf · doi:10.48550/arxiv.1409.1857
A new and simpler definition of a good flag is introduced, and Bott-Samelson varieties are shown to admit such flags
arxiv created 2015/03/30 · arxiv updated 2015/03/31
We use the theory of Mori dream spaces to prove that the global Okounkov body of a Bott-Samelson variety with respect to a natural flag of subvarieties is rational polyhedral. In fact, we prove more generally that this holds for any Mori dream space which admits a flag of Mori dream spaces satisfying a certain regularity condition. As a corollary, Okounkov bodies of effective line bundles over Schubert varieties are shown to be rational polyhedral. In particular, it follows that the global Okounkov body of a flag variety G/B is rational polyhedral. As an application we show that the asymptotic behaviour of dimensions of weight spaces in section spaces of line bundles is given by the counting of lattice points in polytopes.