M 391C Algebraic Geometry (54480)
Dr. Sam Raskin
MWF 9 – 10am
This course is an introduction to algebraic geometry, the study of zero sets of systems of polynomial equations. It is a broad subject, with roots in classical Euclidean geometry and deep ties to number theory and differential geometry. In fact, much of the pre-20th century mathematics we now characterize as algebraic geometry was done by groups of researchers who were not in communication, and who would find each other's work incomprehensible and distant.
We will begin with foundations following Grothendieck's formalism of schemes. We will then focus on algebraic curves, especially the Riemann-Roch theorem and (hopefully) the construction of the Jacobian.
The course will assume some comfort with abstract algebra, especially commutative algebra and the theory of modules over rings. Some familiarity with the basic language of category theory could be helpful, but will not strictly be necessary.