Courses:

Algebraic Geometry >> Content Detail



Syllabus



Syllabus

Amazon logo When you click the Amazon logo to the left of any citation and purchase the book (or other media) from Amazon.com, MIT OpenCourseWare will receive up to 10% of this purchase and any other purchases you make during that visit. This will not increase the cost of your purchase. Links provided are to the US Amazon site, but you can also support OCW through Amazon sites in other regions. Learn more.
Textbook

Amazon logo Mumford, David. The Red Book of Varieties and Schemes. Vol. 1358, Lecture Notes in Mathematics. New York: Springer-Verlag. ISBN: 354063293X.
Includes the Michigan Lectures (1974) on Curves and Their Jacobians.

Homework

There will be weekly homework.

Grading

The course grades will be based on weekly homework and a take home final as shown in table.

ACTIVITIESPERCENTAGES
Weekly Homework80%
Final Exam20%


Prerequisites

Students should have some familiarity with commutative algebra and basic topology. Some more advanced algebraic topology may also be useful as might some knowledge of category theory.

Plan of Course

The aim of this course is to introduce students to some basic notions and ideas in algebraic geometry, paving the way for a study of Grothendiecks's theory of schemes (second semester). Though the theory of schemes and cohomology is generally accepted as the "right" setting for algebraic geometry, these subjects require a substantial amount of technical language which to the uninitiated can sometimes obscure the beauty and elegance of the subject. Thus in an effort to make the subject more accessible and to give students basic techniques without delving into a morass of technical details, I will not use this language in this course but rather the more classical language of varieties, which, though perhaps lacking the elegance of schemes, is perfectly adequate for many situations in algebraic geometry. Thus the goal of the course is more to give students a feeling for algebraic geometry, rather than to develop the foundations of the subject, which students should learn in subsequent courses on schemes.

My plan is to follow somewhat loosely the first chapter of Mumford's book at the begining of the course, and then to discuss the appendix on curves and their Jacobians. Other topics may be included as time permits.

Examples with emphasis on algebraic curves and surfaces are developed. The course may be taken concurrently with 18.705, Commutative Algebra. Knowledge of elementary algebraic topology and elementary differential geometry is recommended, but not required.


 








© 2010-2021 OpenCollege.com, All Rights Reserved.
Open College is a service mark of AmeriCareers LLC.