Professor: Richard Borcherds
Office hours: Tuesday, Thursday 2:00-3:30
927 Evans Hall
Our class meets in TuTh 12:30-02:00P, 81 EVANS. This is the course home page (address
http://math.berkeley.edu/~reb/256A). The course control number is 54451.
Catalogue Description: Mathematics
256A
Three hours of lecture per week. Prerequisites: 250A-250B for 256A; 256A for 256B. Affine and projective algebraic varieties. Theory of schemes and morphisms of schemes. Smoothness and differentials in algebraic geometry. Coherent sheaves and their cohomology. Riemann-Roch theorem and selected applications. Sequence begins fall.
Textbook and course notes:
The textbook is Algebraic geometry
by Hartshorne.
We will cover much of chapters 1 (varieties) and parts of chapters 2 and 4.
.
Background reading
The book Commutative algebra with a view towards algebraic geometry by Eisenbud covers the commutative algebra we need.
The older book Introduction to commutative algebra by Atiyah and Macdonald is also fine.
The ultimate reference is Grothendieck's
FGA,
EGA, and
SGA.
Other online books or notes at about the same level as this course include:
Grading.
Possibly based on homework and a take-home final.
Homework:
The grader for the course is ???. Put homework in his mailbox by Thursday the week after it is assigned.
Links related to the course:
-
The
Macaulay 2 ,
CoCoA,
and
SINGULAR computer packages for commutative algebra.
-
GAGA by Serre,English translation
- Algebraic geometry on wikipedia. See their glossary of classical algebraic geometry if you have ever wondered what a trope or a homaloidal net is.
-
FAC by Serre is an excellent introduction to sheaf cohomology for coherent sheaves.
English translation
- MathOverflow is a good place to ask technical questions about algebraic geometry: it seems to be overrun with people who know EGA off by heart.
- Mathematicians:
Castelnuovo,
Cayley,
Euclid,
Gordan,
Gorenstein,
Grothendieck,
Hensel,
Hilbert,
Hironaka,
Krull,
Kummer,
Lasker,
Macaulay,
Emmy Noether,
Serre,
Sylvester,
Weil,
Weyl,
Zariski
- Tex files of solutions to some of the problems in
Hartshorne's book on algebraic geometry.
1.1
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
4.1.
4.3.