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

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Im M. S., TOSUN M.

AMS Special Session on Inverse Problems, 2022 and AMS Special Session on Geometry and Representation Theory of Quantum Algebras and Related Topics, 2022, Utah, United States Of America, 22 - 23 October 2022, vol.834, pp.53-66, (Full Text) identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 834
  • Doi Number: 10.1090/conm/834/16683
  • City: Utah
  • Country: United States Of America
  • Page Numbers: pp.53-66
  • Keywords: Borel moment map, complete intersection, geometric invariant theory, Grothendieck–Springer resolution, Hilbert scheme, moment map, parabolic moment map, parabolic subgroup, resolution of singularities, singular locus
  • Galatasaray University Affiliated: Yes

Abstract

We study the Borel moment map uB: (formula Presented), given by (formula Presented) and describe an algorithm to explicitly construct the geometric invariant theory (GIT) quotients (formula Presented), and the affine quotient (formula Presented). We also provide an insight of the singular locus of 2n irreducible components of (formula Presented) . Finally, analogous to the Hilbert– Chow morphism, we discuss that the GIT quotient for the Borel setting is a resolution of singularities.