Towards the affine and geometric invariant theory quotients of the Borel moment map
Abstract
We study the Borel moment map μ B : T ∗ ( b × C n ) → b ∗ \mu _B:T^*(\mathfrak {b}\times \mathbb {C}^n)\rightarrow \mathfrak {b}^* , given by ( r , s , i , j ) ↦ [ r , s ] + i j (r,s,i,j)\mapsto [r,s]+ij , and describe an algorithm to explicitly construct the geometric invariant theory (GIT) quotients μ B − 1 ( 0 ) / / det B \mu _B^{-1}(0)/\!/_{\det }B and μ B − 1 ( 0 ) / / det − 1 B \mu _B^{-1}(0)/\!/_{\det ^{-1}}B , and the affine quotient μ B −
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Homotopy and Cohomology in Algebraic Topology
Publication details
- Journal / source
- Contemporary mathematics - American Mathematical Society
- Pages
- 53–66
- Publication date
- 1 January 2026
- Language
- EN