Math 256B - Algebraic Geometry

Instructor	Paul Vojta
Lectures	MWF 11:10–12:00, Evans 3
Class Number	25758
Office	883 Evans
E-Mail:	`vojta@math.berkeley.edu`
Office Hours	MW 1:10--2:00, F 12:10--1:00
Prerequisites	Math 256A
Required Text	Hartshorne, Algebraic Geometry, Springer
Catalog Description	Math 256AB: 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.
Syllabus	We will do some material from Chapter II, if necessary (this is yet to be determined). After that we will do much of Chapter III (Cohomology), followed by some material on smoothness of morphisms.
Grading	Grades will be based on homework assignments. There will be no final exam, but the last problem set will be due sometime during finals week.
Homework	Weekly or biweekly, assigned in class
Comments	I tend to follow the book fairly closely, but try to give interesting exercises and examples.

Handouts

No.	Date	Title	Download
1	February 14	A lemma for the solution of Hartshorne (III, Ex. 4.4)	dvi	pdf
2	February 26	More Information on (III, Ex.~4.4) (revised)	dvi	pdf
3	April 19	Some Lemmas on Curves, and the End of the Proof of (II, 6.8)	dvi	pdf

Homework Assignments

Solutions will be posted on bCourses after each assignment has been graded.

To submit your assignments, use bCourses. I have set it to accept only pdf files.

If you type your homework on the computer (e.g., using LaTeX), then you should be able to create a pdf file directly on the computer and upload it.
If you handwrite your homework, you can use a scanner or your phone's camera to take pictures of your written work, then combine these images into a single PDF file with an app or website such as https://smallpdf.com/jpg-to-pdf.

No.	Due	Assignment		Comments
1	1/31	dvi	pdf
2	2/7	dvi	pdf
3	2/14	Hartshorne III Ex. 2.3, 3.1, 3.2		Ex. 3.2 is (NC)
4	2/21	Hartshorne III Ex. 4.1, 4.3, 4.5		Ex. 4.1 is (NC)
5	2/28	Hartshorne III Ex. 4.7, 5.1
6	3/6	dvi	pdf
7	3/13	dvi	pdf
8	3/20	dvi	pdf
9	4/3	dvi	pdf
10	4/10	dvi	pdf
11	4/17	dvi	pdf
12	4/24	dvi	pdf
13	5/1	dvi	pdf	As announced on bCourses, the third exercise is (NC)
14	5/9	(not yet assigned)

The following policies apply to the homework assignments.

Discussion and the exchange of ideas are essential to doing academic work. For assignments in this course, you are encouraged to consult with your classmates as you work on problem sets. However, after discussions with peers, make sure that you can work through the problem yourself and ensure that any answers you submit for evaluation are the result of your own efforts. In addition, you must cite any books, articles, websites, lectures, etc. that have helped you with your work using appropriate citation practices (other than class lectures and corresponding parts of the textbook). Similarly, you must list the names of students with whom you have collaborated on problem sets. (This paragraph was adapted from http://oue.fas.harvard.edu/icb/icb.do?keyword=k18059&pageid=icb.page498261, accessed on 28 January 2013.)
As an exception to the above, you may not collaborate on problems marked “(nc).”
For problems from the book, you may use without proof any lower-numbered exercises from the same section or any exercises from sections covered earlier. For other exercises, you may use without proof any exercises from earlier sections in the book; for the current section(s), ask. For any exercises, if you weren't able to do an exercise or part of an exercise, you may still assume that it holds for subsequent exercises or parts.
Credit may be reduced if you look up the answer in some other source (as opposed to using the material from elsewhere to aid in your understanding), or if you look ahead in the textbook.

Last updated 24 April 2024