UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

February 13, 2018

939 Evans Hall

3:45PM: How to Count 27 Lines in Macaulay2

Mahrud Sayrafi

In a series of computational examples in Macaulay2, we will give an introduction to Chern classes and projective bundles leading to computing the number of lines on a cubic surface. Specifically, we will see how to define smooth projective varieties in Macaulay2, build vector bundles on them, and use the Schubert2 package to compute their Chern classes. If time permits, we will look at more advance examples in the end. Note: Bring a laptop!

5:00PM: Chern Classes and an introduction to Projective Bundles

Daniel Chupin

In this talk, we will characterize Chern classes of vector bundles on schemes and discuss and invoke the splitting principle as a tool for computing Chern class identities for tensor/wedge/symmetric products of bundles. Time permitting, we may either return to Grassmannians to do some computations or say some words about how Chern classes of the universal bundle generate the Chow ring, or talk about the Chow ring of a projective bundle and its relation to the Chern classes of the underlying vector bundle.

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