Dissertations:
On Fourier-Mukai type functors
Alice Rizzardo
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- Title:
- On Fourier-Mukai type functors
- Author(s):
- Rizzardo, Alice
- Thesis Advisor(s):
- Jong, Aise Johan de
- Date:
- 2012
- Type:
- Dissertations
- Department:
- Mathematics
- Permanent URL:
- http://hdl.handle.net/10022/AC:P:13173
- Notes:
- Ph.D., Columbia University.
- Abstract:
- In this thesis we study functors between bounded derived categories of sheaves and how they can be expressed in a geometric way, namely whether they are isomorphic to a Fourier-Mukai transform. Specifically, we describe the behavior of a functor between derived categories of smooth projective varieties when restricted to the derived category of the generic point of the second variety, when this last variety is a curve, a point or a rational surface. We also compute in general some sheaves that play the role of the cohomology sheaves of the kernel of a Fourier-Mukai transform and are then able to exhibit a class of functors that are neither faithful nor full, that are isomorphic to a Fourier-Mukai transform.
- Subject(s):
- Mathematics
- Item views:
- 121