Fourier-Mukai functors 1000-1M20FM
The lecture is based on [1]. More recent results will also be discussed. The topics covered by the lecture include:
1. Derived categories of coherent sheaves and functors between them.
2. Fourier-Mukai transforms.
3. Equivalences of derived categories of abelian varieties.
4. Exceptional objects, full exceptional collections, Kuznetsov's component.
5. Spherical objects and functors.
6. Spherical functors for flops.
7. McKay correspondence.
8. Categorical resolution of singularities. Noncommutative crepant resolutions.
Type of course
Mode
Requirements
Learning outcomes
Student are acquainted with derived categories of coherent sheaves on algebraic varieties. They are familiar with the most important results in this direction and can comprehend statemets and proofs in publications in this branch of mathematics.
Assessment criteria
The lecture ends with an oral exam. 30 % of the final grade consists of homework and active participation in the exercise sessions.
Bibliography
[1] D. Huybrechts, Fourier-Mukai transforms in algebaic geometry, 2006
Additional information
Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:
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