All the GIT quotients at once

2005/10/03 by Nicholas J. Proudfoot, Proudfoot, Nicholas J.
Mathematics · #14L24 #53D20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.AG #math.SG #msc:14L24 #msc:53D20

paper · pdf · doi:10.48550/arxiv.math/0510055

12 pages, 2 figures; new introduction and conjecture

arxiv created 2006/02/14 · arxiv updated 2009/12/01

Abstract

Let T be an algebraic torus acting on a smooth variety V. We study the relationship between the various GIT quotients of V and the symplectic quotient of the cotangent bundle of V.

Related

• Descent of line bundles to GIT quotients of flag varieties by maximal torus
• Geometric invariant theory and projective toric varieties
• Computation of GIT quotients of semisimple groups
• Chow quotients of ℂ^*-actions
• Smooth torus quotients of Schubert varieties in the Grassmannian