Mathematics 256A Algebraic Geometry Fall 2012

Professor: Richard Borcherds

Office hours: Tuesday, Thursday 2:00-3:30 927 Evans Hall

This class meets in TuTh 12:30-2:00, 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: 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 (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.
  1. August 28-30 1.1, 1.2, 1.3, 1.4, 1.5, 1.6
  2. Sept 4-6 1.7, 1.8, 1.9, 1.11, 1.12
  3. Sept 11, 13 2.1, 2.3, 2.4, 2.5, 2.9
  4. Sept 18-20 2.12, 2.13, 2.14, 2.15, 2.16, 2.17
  5. Sept 25-27 3.1, 3.2, 3.4, 3.5, 3.6, 3.8, 3.11, 3.13
  6. Oct 2-4 3.15, 3.16, 3.17, 3.19, 3.21
  7. Oct 9-11 4.1, 4.4, 4.5,4.6, 4.10
  8. Oct 16-18 5.1, 5.2, 5.3, 5.6, chapter V exercise 5.8b
  9. Oct 23-25 5.8, 5.10, 5.12, 5.14, 5.15
  10. Oct 30-Nov 1 6.1, 6.2, 6.6, 6.7
  11. Nov 6-8 6.3, 6.4, 6.5, Chapter IV Ex 2.5
  12. Nov 13-15 Chapter II 1.1, 1.3, 1.8, 1.13, 1.18,
  13. Nov 20 Chapter II 2.2, 2.5, 2.6, 2.9, 2.10, 2.11,
  14. Nov 27-29 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: