Algebraic Curves
This course is a followup 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: 2:303:45 TuTh on Zoom Office Hours: After the lecture  
Topics  Handwritten Notes  

Introduction 
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, RiemannHurwitz 
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 