Towards the affine and geometric invariant theory quotients of the Borel moment map

2020/01/27 by Im, Mee Seong, Tosun, Meral
#Algebraic Geometry (math.AG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2001.09701

Abstract

We study the Borel moment map μ_B:T^*(\mathfrakb× ℂⁿ)→ \mathfrakb^*, given by (r,s,i,j)↦ [r,s]+ij, and describe our algorithm to construct the geometric invariant theory (GIT) quotients μ_B^-1(0)/ /_detB and μ_B^-1(0)/ /_det^-1B, and the affine quotient μ_B^-1(0)/ /B. We also provide an insight of the singular locus of 2ⁿ irreducible components of μ_B. Finally, analogous to the Hilbert--Chow morphism, we discuss that the GIT quotient for the Borel setting is a resolution of singularities.

Related

• Moment maps and geometric invariant theory
• Moment Maps, Strict Linear Precision, and Maximum Likelihood Degree One
• The moment-weight inequality and the Hilbert-Mumford criterion
• The MMP singularities of GIT versus Baily-Borel compactifications for the ball quotient case
• Refinements of the Morse stratification of the normsquare of the moment map