Fall 2008
Professor: Hal Schenck
332 Illini
Office hours: TBA, and by appointment.
Phone: 333-2229.
E-mail: schenck@math.uiuc.edu.
Meeting times/rooms
TR 12:00-1:20
Course Description. Algebraic curves are the first main class of examples studied in algebraic geometry. They can be studied from a variety of viewpoints, with the two main approaches being via commutative algebra (as in Fulton's book "Algebraic Curves") and complex analysis (as in Griffiths book "Algebraic Curves"). However, it is the interplay between viewpoints that makes them so interesting. This course will be an introduction to algebraic geometry, which uses algebraic curves as the main examples.
Official description: an introduction to Riemann Surfaces from both the algebraic and function-theoretic points of view. Topics include projective algebraic curves, differential forms, integration, divisors of poles and zeroes, linear systems, the Riemann-Roch theorem, Serre duality, and applications. Prerequisite: MATH 500 and MATH 542.
Text. Algebraic curves and Riemann surfaces Miranda
Grading. Your grade will be determined by class participation and homework, which will be collected every two weeks. I expect that the amount of time you spend outside of class on this course to be about 5 hours/week, with 3 hours devoted to reading before class, and 2 hours to working on suggested problems.