
Date 
Topic 
Book 
Homework 
Jan. 
7 
What is algebraic geometry? 



8 
Shapes, functions and pullbacks 



10 
Faithfullness of pullbacks 



14 
Affine algebraic varieties 
§1.2 


15 
Computing in quotient rings 

H1 

17 
Morphisms of affine varieties 

A1 

21 
More on morphisms 



22 
Categories, functors, and isomorphisms 

H2 

24 
Discussion of projects 

A2 

28 
Ideals and radicals 



29 
Maximal ideals in quotient rings 

H3 

31 
The Nullstellensatz 
§4.1 
A3 
Feb. 
4 
The ideal/subvariety correspondence 
§4.2 


5 
Chain conditions 

H4 

7 
The Zariski topology 
§4.4 
A4 

11 
More on the Zariski topology 



12 
Principal open sets 

H5 

14 
Functions and patching 

A5 

18 




19 
Reading Week




21 




25 
Sheaves of functions 



26 
Projective Space 
§8.2 
H6 

28 
More about P^{2} 

A6 
Mar. 
4 
Homogeneous polynomials 



5 
Homogenization and dehomogenization 

H7 

7 
Projective varieties 
§8.2 
A7 

11 
Cones; singularities of hypersurfaces 



12 
Geometry of plane curve singularities 

H8 

14 
The genus of degree d plane curves I 

A8 

18 
The genus of degree d plane curves II 



19 
Maps between Riemann surfaces 

H9 

21 
The topology of maps between Riemann surfaces I 

A9 

25 
The topology of maps between Riemann surfaces II 



26 
The RiemannHurwitz formula 

H10 

28 
Consequences of the RiemannHurwitz formula 

A10 
Apr. 
1 
The group law on an elliptic curve 



2 
A theorem of Poncelet 

H11 

4 
Polynomial solutions to polynomial equations 

A11 

8 




9 


H12 

11 


A12 