Chow Groups and Algebraic Cycles in Complex Algebraic Geometry - Part 3

Explore complex algebraic geometry in this advanced mathematics lecture focusing on Chow groups, presented by UCLA's Burt Totaro at the IAS PCMI Park City Mathematics Institute. Dive into the relationship between complex algebraic varieties and complex manifolds, examining how algebraic subvarieties represent cohomology classes. Learn about the fundamental concept of Chow groups in algebraic varieties over any field, their similarities to homology and cohomology groups, and their computational challenges related to the Hodge conjecture. Discover how this theory serves as a bridge between homotopy theory and algebraic geometry, connecting to advanced concepts like algebraic K-theory, motivic cohomology, and algebraic cobordism. Study divisors and line bundles as foundational elements, with special attention to their behavior in singular varieties. Access complementary materials including lecture notes, problem sets, and recommended readings from key texts like Hartshorne's Algebraic Geometry, Fulton's Intersection Theory, and Eisenbud-Harris's 3264 and All That.