Algebraic Curves

This course is a follow-up to last semester's course on Commutative Algebra. See the typed lecture notes.

This semester we will cover "one dimensional mathematics." This is based on the amazing 19th century synthesis of three seemingly different subjects:

- Algebraic Curves: Sets in the plane defined by a single polynomial equation f(x,y)=0.
- Riemann Surfaces: One dimensional compact complex manifolds.
- Function Fields: Field extensions over the complex numbers of transcendence degree one.

Lecture: 2:30--3:45 TuTh on Zoom
Office Hours: After the lecture
Topics Handwritten Notes
Jan 25 Notes
Jan 26 Notes
Jan 28 Notes
Zariski Topology
Homework 1
Feb 2 Notes
Feb 4 Notes
Projective Geometry
Feb 9 Notes
Feb 11 Notes
Feb 16 Notes [Maple Worksheet]
Singular Points
Feb 18 Notes
Feb 23 Notes
Feb 25 Notes
Bezout's Theorem
Mar 2 Notes
Mar 4 Notes
Applications of Bezout
Homework 2
Mar 9 Notes
Mar 11 Notes
Cubic Curves
Mar 16 Notes [Maple Worksheet]
Mar 18 Notes
Idea of a Riemann Surface
Mar 23 Notes
Mar 25 Notes
Mar 30 Notes
Meromorphic Functions,
Apr 1 Notes
Apr 6 Notes
Harnack's Theorem,
Segre Embedding
Apr 8 Notes
Apr 13 Notes
Apr 15 Notes
Secant Variety,
Function Field,
Ran Out of Time
Apr 20 Notes
Apr 22 Notes
Apr 27 Notes