2001/05/31 by Michel Brion, Brion, Michel · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #math.AG #math.KT #msc:14C35 #msc:14M15
paper · pdf · doi:10.48550/arxiv.math/0105254
AMSLaTeX; 21 pages
arxiv created 2001/05/31 · arxiv updated 2009/11/30
We prove a conjecture of A. S. Buch concerning the structure constants of the Grothendieck ring of a flag variety with respect to its basis of Schubert structure sheaves. For this, we show that the coefficients in this basis of the structure sheaf of any subvariety with rational singularities, have alternating signs. Equivalently, the class of the dualizing sheaf of such a subvariety is a nonnegative combination of classes of dualizing sheaves of Schubert varieties.