Math 256B  Algebraic Geometry
Instructor  Paul Vojta 
Lectures  MWF 1:10–2:00, online 
Class Number 
22869 
Office  883 Evans 
EMail:  vojta@math.berkeley.edu 
Office Hours  TBD 
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.
RiemannRoch theorem and selected applications. Sequence begins fall.

Syllabus  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 about
a week after the last day of classes. 
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
There are no handouts yet.
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/jpgtopdf.
1  2/1 
dvi 
pdf 
2  2/8 
dvi 
pdf 
3  2/16 
Hartshorne III Ex. 2.3, 3.1, 3.2 3.2 is (NC) 
4  2/24 
Hartshorne III Ex. 4.1, 4.3, 4.5 4.1 is (NC) 
5  3/4 
dvi 
pdf 
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
lowernumbered 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 25 February 2021