Professor: Richard Borcherds
Office hours: Tuesday, Thursday 2:003:30
927 Evans Hall
This class meets in TuTh 12:302:00, 81 EVANS. This is the course home page (address
http://math.berkeley.edu/~reb/256A).
Catalogue Description: Mathematics
256A
Three hours of lecture per week. Prerequisites: 250A250B 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. RiemannRoch 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 (schemes) and 4 (curves).
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.
Homework:
There is no grader for this course so there is no point in handing homework in. The following homework is just a suggestion for those who like to have homework assigned.
 August 2830 1.1, 1.2, 1.3, 1.4, 1.5, 1.6
 Sept 46 1.7, 1.8, 1.9, 1.11, 1.12
 Sept 11, 13 2.1, 2.3, 2.4, 2.5, 2.9
 Sept 1820 2.12, 2.13, 2.14, 2.15, 2.16, 2.17
 Sept 2527 3.1, 3.2, 3.4, 3.5, 3.6, 3.8, 3.11, 3.13
 Oct 24 3.15, 3.16, 3.17, 3.19, 3.21
 Oct 911 4.1, 4.4, 4.5,4.6, 4.10
 Oct 1618 5.1, 5.2, 5.3, 5.6, chapter V exercise 5.8b
 Oct 2325 5.8, 5.10, 5.12, 5.14, 5.15
 Oct 30Nov 1 6.1, 6.2, 6.6, 6.7
 Nov 68 6.3, 6.4, 6.5, Chapter IV Ex 2.5
 Nov 1315 Chapter II 1.1, 1.3, 1.8, 1.13, 1.18,
 Nov 20 Chapter II 2.2, 2.5, 2.6, 2.9, 2.10, 2.11,
 Nov 2729 Chapter II 3.1, 3.2, 3.3, 3.5, 3.9, 3.11, 3.15, 3.18
Tex files of solutions to some of the homework problems:
1.1
1.2.
1.3.
1.4.
1.5.
1.6.
1.7.
4.1.
4.3.
Links related to the course:

The
Macaulay 2 ,
CoCoA,
and
SINGULAR computer packages for commutative algebra.
 Algebraic geometry on wikipedia. See their glossary of classical algebraic geometry if you have ever wondered what a trope or a homaloidal net is.
 MathOverflow is a good place to ask technical questions about algebraic geometry.
 Mathematicians:
Castelnuovo,
Cayley,
Enriques,
Euclid,
Gordan,
Gorenstein,
Grothendieck,
Hensel,
Hilbert,
Hironaka,
Krull,
Kummer,
Lasker,
Macaulay,
Emmy Noether,
Max Noether,
Riemann,
Serre,
Sylvester,
Weil,
Weyl,
Zariski