Department of Mathematics Syllabus

This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.

MAT 248B: Algebraic Geometry
Approved: 2009-05-01, Eric Babson, Motohico Mulase, Brian Osserman

Units/Lecture:

Winter, alternate years; 4 units; lecture/extensive problem solving

Suggested Textbook: (actual textbook varies by instructor; check your instructor)
Algebraic Geometry, Robin Hartshorne, ISBN 978-0-387-90244-9 ($69); Alternate: Basic Algebraic Geometry 2, Shafarevich, ISBN-13: 978-3540575542 ($69)

Prerequisites:

MAT 248A

Course Description:

Complex varieties and the analytic topology. Sheaves and schemes. Fiber products. Separatedness and properness. Applications of scheme theory.

Suggested Schedule:


Lectures Sections Topics/Comments
1 - 8 Appendix B Complex varieties and the analytic topology; a sampling of classical applications.
9 -18 II.1 - II.4 Basics of sheaves and schemes; fiber products, separatedness and properness.
19 - 28 N/A Applications of scheme theory.

Additional Notes:

Possibilities for applications of scheme theory include: representable functors and moduli spaces, fibers of morphisms of Dedekind schemes, non-reduced schemes and intersection multiplicity, and deformation theory. Many of these topics as well as much of the material on complex varieties require supplemental material beyond that in Hartshorne.