Descent of line bundles to GIT quotients of flag varieties by maximal torus

2007/02/19 by Shrawan Kumar, Kumar, Shrawan
Mathematics · #14L24 #14L30 #57S25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Group Theory (math.GR) #math.AG #math.GR #msc:14L24 #msc:14L30 #msc:57S25

paper · pdf · doi:10.48550/arxiv.math/0702556

19 pages

arxiv created 2007/02/19 · arxiv updated 2009/12/01

Abstract

Let L be a homogeneous ample line bundle on any flag variety G/P and let T be a maximal torus of G. We prove a general necessary and sufficient condition for L to descend as a line bundle on the GIT quotient of G/P by T. We use this result to explicitly determine exactly which L descend to the GIT quotient for any simple complex algebraic group G and any parabolic subgroup P.

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