Math 256B - Section 1 - Algebraic Geometry

Instructor: Brian Osserman

Lectures: TuTh 2:00-3:30pm, Room 72 Evans

Course Control Number: 54982

Office: 767 Evans, e-mail:

Office Hours: Tu 1:00-2:00, W 2:00-3:00 (this week only: instead of W, office hour Th 11:30-12:30)

Prerequisites: 256A

Required Text: Hartshorne, Algebraic Geometry

Recommended Reading: Eisenbud and Harris, the Geometry of Schemes

Syllabus: This is the second semester of an integrated, year-long course in algebraic geometry. The primary source text will be Hartshorne's Algebraic Geometry. We will have already covered most of Chapter II in the fall. We will begin with the basic properties of sheaf cohomology and the statement of the Riemann-Roch theorem, and classical applications to the study of curves. This will serve as motivation for the development of cohomology in Chapter III. Some important topics from projective geometry that were skipped in the fall will be worked in as appropriate. Finally, we will conclude with some discussion of special topics, most likely involving moduli spaces.

Grading: 75% homework, 25% final paper

Homework: Homework will be assigned roughly weekly


Welcome to Math 256B: Algebraic Geometry

Homework assignments and supplementary notes, as well as lecture synopses, will be posted here as the course progresses. For general comments, please see last semester's course web page.


Problem sets

Problem sets will be posted here, due on Tuesdays. Problems will be frequently assigned out of Hartshorne, so if you don't have your own copy, be ready to get problems from the library before it closes for the weekend. You may use any results from Hartshorne unless they trivialize the problem or use machinery which we have not introduced.


Final paper guidelines

The purpose of the final paper is twofold: to learn in detail about a topic not covered in class, and to practice mathematical writing. As such, it will be graded as much on clarity of writing as on any other factors.

Guidelines:

Possible topics: you are free to choose any topic in algebraic geometry which interests you. If you have something in mind, that's great. If not, the following areas would offer plenty of good paper topics:


Lectures

I will post here a synopsis of each lecture, including the sections in Hartshorne covered, and/or any supplemental notes.


Cheat sheets

This is a collection of cheat sheets, which are designed to serve two main purposes: first, to help organize all the definitions and basic results involving properties and schemes and morphisms, and second, to include statements and references for more general results when Hartshorne only states them under unnecessarily restrictive hypotheses.

These will be updated and expanded as we cover additional material.