This course provides an introduction to algebraic geometry. Algebraic
geometry is a central subject in modern mathematics, and an
active area of research. It has connections with
number theory, differential geometry, symplectic geometry, mathematical
physics, string theory, representation theory, combinatorics and others.
Math 203 is a three quarter sequence. Math 203a will serve as
preparation for a course in scheme theory (which may be covered in Math
203bc). Math 203bc will be taught by Professor Mark Gross in the Winter
and Spring quarters.
We will study affine and projective algebraic varieties,
and their properties. Among others, we will consider concepts such as
smoothness, singularities, dimension, intersection multiplicities. I hope
to illustrate the general theory with many examples. The goal is to cover
roughly the first chapter (+epsilon) of Hartshorne's book.