2012 Theses Doctoral

# On Fourier-Mukai type functors

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.

## Files

- Rizzardo_columbia_0054D_10738.pdf application/pdf 410 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Jong, Aise Johan de
- Degree
- Ph.D., Columbia University
- Published Here
- May 7, 2012