MAS 5932
ALGEBRAIC GEOMETRY I
Fall 2008

Instructor: Amod Agashe Email: agashe@math.fsu.edu
Office: 216 LOV Phone: 644-8704
Web page: http://www.math.fsu.edu/~agashe/ag.html
Office Hours: To be announced.

Recommended text. Hartshorne, Algebraic geometry.
Prerequisities. A year long sequence in graduate algebra, e.g., GRV-I and II. If you are taking the GRV sequence in parallel, you should be able to get started with this course, but may need to do some extra reading. In any case, you should be comfortable working with groups, rings, ideals, and preferably with modules. Field theory (including Galois theory) is not needed as such.
Course description. Algebraic geometry started off by studying solutions of certain polynomials, which are called varieties. One then studies maps between such objects, properties of such objects and of the maps between them, etc. In more recent times, this theory was vastly generalized to associate to collections of rings certain geometric objects called schemes. Much of the theory of varieties generalizes to schemes; however things get technically complicated. The theory of schemes has become the accepted common language in algberaic geometry these days. In this course, we will study varieties and schemes almost in parallel, using varieties to get the geometric intuition and schemes to get the algebraic finesse. The goal is to learn the language and some of the major results. Thus we will focus on breadth rather than depth, skipping proofs for the most part. The topics to be covered include varieties, schemes, morphisms, basic properties and geometry of varieties and schemes, sheaf cohomology and Serre duality (in particular the Riemann-Roch theorem). The sections to be covered from the text are roughly I.1 to I.3, II.1 to II.8, III.1 to III.7, and IV.1. It is not clear how much of this material we will cover. If needed some of it may get postponed to a topics course in Spring 2009.
Grading. The grade will be based on homeworks and class attendance.
Honor Code. The Academic Honor System at The Florida State University is based on the premise that each student has the responsibility 1) to uphold the highest standards of academic integrity in the student's own work, 2) to refuse to tolerate violations of academic integrity in the University community, and 3) to foster a high sense of integrity and social responsibility on the part of the University community. A copy of the University Academic Honor Code can be found in the current Student Handbook and you are bound by it in all your academic work.
American Disabilities Act. Students with disabilities needing academic accommodations should register with and provide documentation to the Student Disability Resource Center (SDRC), and bring a letter from the SDRC to the instructor indicating their needs.This should be done within the first week of class.