Syzygies of some GIT quotients

2013/09/16 by Krishna Hanumanthu, Hanumanthu, Krishna, S. Senthamarai Kannan +1
Mathematics · #13D02 #14L24 #14L30 #14M15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:13D02 #msc:14L24 #msc:14L30 #msc:14M15

paper · pdf · doi:10.48550/arxiv.1309.3893

11 pages; improved bounds in main results; new references added

arxiv created 2015/07/24 · arxiv updated 2015/07/27

Abstract

Let X be flat scheme over ℤ such that its base change, X_p, to \mathbbF_p is Frobenius split for all primes p. Let G be a reductive group scheme over ℤ acting on X. In this paper, we prove a result on the N_p property for line bundles on GIT quotients of X_ℂ for the action of G_ℂ. We apply our result to the special cases of (1) an action of a finite group on the projective space and (2) the action of a maximal torus on the flag variety of type A_n.

Related

• Syzygies of Line Bundles on GIT Quotients
• The GIT-equivalence for G-line bundles
• Recognizing flag varieties and reductive groups
• Descent of line bundles to GIT quotients of flag varieties by maximal torus
• Computation of GIT quotients of semisimple groups