Math 763: Algebraic Geometry

This is the basic introductory course in algebraic geometry. We will cover the material in the first chapter of Hartshorne's "Algebraic Geometry" book (GTM 52), but with multiple detours to cover more examples (the main weakness of Hartshorne's book is the lack of examples). Other texts that we may use briefly are Joe Harris's book "Algebraic Geometry" (GTM 133) and/or Miles Reid's introductory book. So our main object of study will be varieties (not schemes) over an algebraically closed field, and we won't be touching at all on cohomology of sheaves.

Familiarity with commutative algebra and algebraic topology will be useful, but not absolutely required. A general grasp of abstract algebra will be needed, though. The pace of the course will be mainly determined by the students, so I encourage anyone who is interested to attend the first few lectures and decide if it is at their level or not.