Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring: Introduction to Deformation Theory

Seminar | October 17 | 5-6 p.m. | 939 Evans Hall

 Ritvik Ramkumar, UC Berkeley

 Department of Mathematics

In the first talk I will give an introduction the notion of a deformation, give examples and explain why deformations can fail to exist. This will include deformations of k-algebras (varieties) and modules over a fixed algebra (coherent sheaves). I will end by describing how deformation theory is used to understand the global geometry of the Hilbert Scheme. In particular, motivate why the Hilbert scheme parameterizing nice objects can be badly behaved.