Schubert Calculus Learning Seminar

Meetings at 15:00 on Thursdays, STEM 565

Welcome! Here are some useful resources:

• 3264 and All That: Intersection Theory in Algebraic Geometry by Eisenbud and Harris
• Some other useful books:
  • Harris Algebraic Geometry: A First Course
  • Hartshorne Algebraic Geometry
  • Eisenbud Commutative Algebra with a View Towards Algebraic Geometry
  • Fulton Intersection Theory
• A review of Intersection Theory by Kleiman which gives a short history of the subject

A conic (the red one) tangent to 5 general conics (the blue ones) in the plane. It turns out there are exactly 3264 such (red) conics. This result (due to Chasles) is the namesake of the book. Image source

Lectures

2025-02-06: Overview of the subject, introduced projective space.

2025-02-17: Affine algebraic sets, Zariski topology and the Nullstellensatz, details in Hartshorne I.1. Digression on vector bundles, see here for classification of line bundles on the circle.

2025-02-27: Regular functions and morphisms, category of quasi-projective varieties, maybe fibre products. References: Hartshorne I.2-3.

There were 3 more sessions, though they were not recorded here at the time. In the end we covered the Chow ring of Gr(2,4) and used this to compute the number of lines meeting 4 lines in general position in projective space.

...