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.