Introduction to Algebraic Geometry 5020

Instructor: Milena Hering
Class time and room: Tuesday and Thursday 12:30 - 1:45 in MSB 117.
Office: MSB M322

Office hours: Tuesday 10:45 - 11 AM and 2-3 PM, by appointment, or whenever I am in my office.
Phone:486-3120
E-mail: hering@math.uconn.edu

The Twisted cubic.

Check out a video of the blow up at a point.

Homework 1
Homework 2
Homework 3
Homework 4 or as tex-file.
Homework 5 or as tex-file.
Homework 6 or as tex-file.
Homework 7.
Hence some working knowledge in algebraic geometry is useful in many different contexts.

We will introduce basic concepts in algebraic geometry, such as affine and projective varieties, Hilbert's Nullstellensatz, Zariski topology, regular functions, the Zariski tangent space, smoothness, degree, the Hilbert polynomial, rational maps, divisors, line bundles and maps to projective spaces. We will finish with the Riemann-Roch theorem for curves. We will illustrate these concepts with many examples, such as projective spaces, Grassmannians, products of projective spaces, Segre and Veronese embeddings, and blow-ups.

The prerequisite for this class is completion of the algebra sequence (5210, 5211). Background in commutative algebra will be reviewed as needed. It might be useful to do a few exercises from Atiyah - Macdonald's book. There is not a single text book for this class. The main reference will be the notes you take in class.

Here is a list of references for this class:
Fulton: Algebraic Curves .
Gathmann: lecture notes.
Harris: "Algebraic Geometry - a first course".
Hartshorne: "Algebraic Geometry".
Shafarevich: "Basic Algebraic Geometry" (Volume 1).