Math 413/813 — Introduction to Algebraic Geometry


Algebraic Geometry is a subject whose rich origins include greek geometry, the analytic geometry of Descartes, and the mathematical foundations of perspective drawing. Its powerful modern tools allow a synthesis of algebra, geometry, topology, and number theory, and are used in many other parts of mathematics.

At its heart algebraic geometry contains a vast dictionary between geometric ideas and algebraic ones. The dictionary allows algebraic geometry to play the role of a mathematical crossroads where many areas of mathematics meet and enrich each other.

This course is an introduction to algebraic geometry, intended for graduate and upper year students in Mathematics. We will build up the fundamental geometric objects — affine and projective varieties — and explore their basic properties. Along the way we will study the first entries in the algebraic/geometric dictionary, make detours through algebra, topology, and geometry, and see many beautiful examples and constructions.

Instructor: Mike Roth
Office Hours: Wednesdays 17:30—18:30,   Fridays 14:30—15:30  (both in Jeff 201),   or by appointment.
Textbook: Ideals, Varieties, and Algorithms, by Cox, Little, and O'Shea, third edition, Springer-Verlag, 2007. A pdf copy of the book may be downloaded for free through the Queens library.
Other references:
1. Algebraic Geometry, a first course, by J. Harris, Springer-Verlag, 1992.
2. Introduction to Algebraic Geometry, by B. Hassett, Cambridge University Press, 2007.

Classes (slot 3)
  Mon. 10:30–11:30   Wed. 9:30–10:30   Fri. 8:30–9:30
  All classes are in Jeff 115.

Grading Scheme
Homework 60%
Project 40%

There are twelve homework assignments during the semester. The lowest two of these twelve grades will be dropped when computing the homework grade for the course.

Further details about the projects may be found on the 'projects' page.