Math 413/813 — Introduction to Algebraic Geometry


  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 P2 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 Riemann-Hurwitz formula H10
31 Consequences of the Riemann-Hurwitz 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