Syllabus - Mathematics 137: Algebraic Geometry; Spring 2008

Mathematics 137: Algebraic Geometry Harvard University Spring 2008
Course homepage
Meets: MWF at 2pm in SC 216
Instructed by: John F. Duncan Harvard University Department of Mathematics One Oxford Street Cambridge, MA 02138 U.S.A.
Office: Phone: Web: Email:	SC 320 (617) 495 5377 math.harvard.edu/~jfd/ duncan (at) math
Course Assistant: Silas Richelson Email: sirichel (at) fas
Page last revised: January 30th, 2008

Syllabus
Description Mathematics 137: *Algebraic geometry*, is an introduction to the basic notions of algebraic geometry, with a particular focus on algebraic curves.
Texts Phillip A. Griffiths, Introduction to Algebraic Curves, American Mathematical Society, 1989. Frances Kirwan, Complex Algebraic Curves, Cambridge University Press, 1992.
Contents The course opens with fundamentals concerning complex algebraic curves and Riemann surfaces. We then establish the Normalization Theorem, which is a key step in analyzing the deep relationships between these two classes of objects. Applications of the Riemann-Roch Theorem, which relates the analytic properties of a Riemann surface to its purely topological properties, are a highlight of the course. We conclude with the Abel-Jacobi Theorem, which facilitates further applications of algebraic curves, and connects with the theories of elliptic curves and elliptic integrals. Click here for a more detailed outline of the course contents.
Prerequisites The main prerequisite is Mathematics 123, which is a second semester course in abstract algebra that introduces the theory of rings and fields. Familiarity with the basics of complex analysis, such as are covered in Mathematics 113, will also be useful.
Homework Weekly homework assignments will be due on the Wednesday of the week following that in which they are assigned. Collaboration between students is encouraged, but you must write your own solutions, and you must give credit to your collaborators. Late homework will not be accepted.
Midterm There will be one in-class midterm, on Friday, March 14th.
Final There will be a take-home final, which will be assigned at 5pm on Tuesday, May 6th, and will be due at 5pm on Friday, May 9th. Collaboration on the final will not be permitted, but you will be free to refer to, and quote, your course notes and the texts for the course.
Assessment Final grades will be based on regular weekly homework (40%), the midterm (20%) and the final (40%).