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Monthly Archives: July 2014

Addendum to last post: the total Chern classes of tautological bundles on G(k,n)

I realised after finishing the last post that it’s simpler than I had thought to compute the total Chern classes of the tautological bundles appearing in the short exact sequence

0 \to \mathcal{S} \to \mathbb{C}^n \to \mathcal{Q} \to 0

on the Grassmannian G(k,n). I’m keeping it in a separate post, though, both because the last post is already very long and because I haven’t yet defined the Schubert varieties that appear in the answer.

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Schubert Calculus I: Geometry of G(k,n)

Goals for this post:

  • coordinate systems
  • line and vector bundles and divisors
  • the functor of points perspective
  • the homogeneous coordinate ring is a UFD

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Schubert Calculus Mini-Course

Next week, I am teaching a mini-course, introducing some of my fellow UM grad students to Schubert calculus. It will focus on the Grassmannian. Ultimately, I also hope to have all the notes from the course posted on this blog.

My goal is to help both my combinatorially- and geometrically-oriented friends learn enough of both toolsets to carry out concrete computations in intersection theory.

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