Math 207 - Topics in Algebraic Geometry: Derived Categories

Contact Info:

Dragos Oprea, APM 6-101, doprea at math dot ucsd dot edu.


WF 10-11:20 in APM B412.

Course description:

The first half of the course will introduce the derived category of sheaves and derived functors. For any algebraic variety, the derived category of sheaves is a complicated invariant which is quite difficult to calculate explicitly, but which contains a lot of information about the original geometric object. In particular, one may try to determine when two algebraic varieties have equivalent derived categories. For instance, Mukai proved that an abelian variety and its dual have equivalent derived categories. This equivalence (and its generalizations) is now called the Fourier-Mukai transform. Fourier-Mukai transforms will be discussed in the second half of the course, together with applications to moduli spaces of sheaves, birational geometry, mirror symmetry and others.


I will assume background in algebraic geometry at the level of Math 203. Beyond Math 203, I will make an attempt to keep the course reasonably self-contained.

Office hours:

W 11:30-12:30. I am available for questions after lecture or by appointment. Also, feel free to drop in if you see me in my office.


The course is intended for advanced graduate students in Mathematics. There will be no homework or exams for this course if you are a math graduate student; the grade will be based only on attendance.


There will be no lecture Friday April 13 (because of WAGS in Seattle). We will make up for it on Monday April 16.

Class time and location have changed: WF 10-11:20 in B412.

Lecture Summaries: