Math 256B - Algebraic Geometry
|Lectures||MWF 1:10–2:00, online|
|Required Text||Hartshorne, Algebraic Geometry,
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 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.|
||Weekly or biweekly, assigned in class|
|Comments||I tend to follow the book fairly closely,
but try to give interesting exercises and examples.|
There are no handouts yet.
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
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||Hartshorne III Ex. 2.3, 3.1, 3.2|
3.2 is (NC)
||Hartshorne III Ex. 4.1, 4.3, 4.5|
4.1 is (NC)
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
accessed on 28 January 2013.)
- As an exception to the above, you may not collaborate on problems
- 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
- 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