2022-01-28

Tags: #untagged

Refs: ?

15:11

  • Bott-Samelson manifold: lists of flags starting at the base flag \(B/B\) only changing by a little bit at each step.
  • It’s an iterated \({\mathbb{P}}^1\) bundle, hence smooth projective irreducible with a \(B\) action. \(\BS^Q\) associated to a word \(Q\) in the Weyl group.
  • Bott-Samelson map \(\BS^Q \to G/B\): send a flag to the top space, its image is some \(B{\hbox{-}}\)orbit closure \(X^w = { \operatorname{cl}} (BwB)/B\), i.e. a Schubert variety. Yields that \(\BS^Q \to X^w\) is a resolution of singularities, the advantage is that it’s combinatorially easy to understand. Rational, degree 1.
  • What is a moment map?
  • What is a stratification?
#web/quick_notes #untagged