Algebraic Geometry Working Seminar

Austin Sun, Department of Pure Mathematics, University of Waterloo

"Two Proofs of the Generalized Bézout's Theorem - Part II"

In the second part of this talk series, I will focus on the algebraic aspects of the generalized Bézout's theorem. Specifically, I will give the definition of the degree of algebraic varieties using Hilbert polynomials. Then, I will give an overview of intersection multiplicities and discuss intuitions behind their definition. Finally, I will present a version of the generalized Bézout's theorem using the language of intersection multiplicities, and give a proof as found in Algebraic Geometry by Robin Hartshorne. If I have time, I will compare the two different proofs that I presented and discuss some geometric and algebraic intuitions behind the generalized Bézout's theorem.

This seminar will be held jointly online and in person:

• Room: MC 5403
• Zoom information: Meeting ID: 817 1030 9714; Passcode: 063438