Neena Gupta- The Zariski Cancellation Problem and Related Problems in Affine Algebraic Geometry

Explore the Zariski Cancellation Problem and related topics in Affine Algebraic Geometry in this 40-minute lecture by Neena Gupta. Delve into the intricacies of Affine Spaces, Polynomial Rings, and the Asanuma Ring. Examine the Affine Fibration Problem and its theorems, along with the Epimorphism Problem for Hyperplanes. Investigate examples such as the Russell-Koras threefolds and the Bhatwadekar-Dutta case. Gain insights into the Derksen invariant and the Segre-Nagata lines, enhancing your understanding of complex algebraic concepts.

Syllabus

Intro
Zariski Cancellation Problem on Affine Spaces
ZCP on Polynomial Rings
Asanuma Ring (1987)
Affine Fibration Problem: Some Theorems
Asanuma ring and Segre-Nagata lines
Epimorphism Theorem
Epimorphism Problem for Hyperplanes
Epimorphism Problem: Russell-Sathaye, Kalima
An example of Russell-Koras threefolds
Derksen invariant
An Example of Bhatwadekar-Dutta (1993)