
Date 
Topic 
Book 
Homework 
Jan. 
9 
What is algebraic geometry? 



11 
Shapes, functions and pullbacks 



13 
Faithfullness of pullbacks 



16 
Affine algebraic varieties 
§1.2 


18 
Computing in quotient rings 

H1 

20 
Morphisms of affine varieties 

A1 

23 
More on morphisms 



25 
Categories, functors, and isomorphisms 

H2 

27 
Discussion of projects 

A2 

30 
Ideals and radicals 


Feb. 
1 
Maximal ideals in quotient rings 

H3 

3 
The Nullstellensatz 
§4.1 
A3 
Feb. 
6 
The ideal/subvariety correspondence 
§4.2 


8 
Chain conditions 

H4 

10 
The Zariski topology 
§4.4 
A4 

13 
More on the Zariski topology 



15 
Principal open sets 

H5 

17 
Functions and patching 

A5 

20 




22 
Reading Week




24 




27 
Sheaves of functions 


Mar. 
1 
Projective Space 
§8.2 
H6 

3 
More about P^{2} 

A6 

6 
Homogeneous polynomials 



8 
Homogenization and dehomogenization 

H7 

10 
Projective varieties 
§8.2 
A7 

13 
Cones; singularities of hypersurfaces 



15 
Geometry of plane curve singularities 

H8 

17 
The genus of degree d plane curves I 

A8 

20 
The genus of degree d plane curves II 



22 
Maps between Riemann surfaces 

H9 

24 
The topology of maps between Riemann surfaces I 

A9 

27 
The topology of maps between Riemann surfaces II 



29 
The RiemannHurwitz formula 

H10 

31 
Consequences of the RiemannHurwitz formula 

A10 
Apr. 
3 
The group law on an elliptic curve 



5 
A theorem of Poncelet 

H11 

7 
Polynomial solutions to polynomial equations 

A11 

10 




12 


H12 

14 


A12 