Introduction to Chow Groups in Algebraic Geometry - Part 2

Explore complex algebraic geometry in this advanced mathematics lecture focusing on Chow groups and their computational aspects. Learn how complex algebraic varieties function as complex manifolds and topological spaces, with emphasis on which cohomology classes can be represented by complex algebraic subvarieties. Dive into the theory of algebraic cycles and the Hodge conjecture - one of mathematics' million-dollar problems. Master the concept of Chow groups for algebraic varieties over any field, understanding their formal properties similar to homology or cohomology groups while built directly from algebraic subvarieties. Examine divisors and line bundles as foundational elements, particularly their behavior in singular varieties. Study from recommended texts including Hartshorne's Algebraic Geometry, Fulton's Intersection Theory, and Eisenbud-Harris's 3264 and All That, while engaging with provided lecture notes and problem sets. Part of the 2024 Program on Motivic Homotopy Theory, this lecture requires background knowledge in algebraic geometry, algebraic topology, and homotopy theory.