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On Fourier-Mukai type functors

Alice Rizzardo

Title:
On Fourier-Mukai type functors
Author(s):
Rizzardo, Alice
Thesis Advisor(s):
Jong, Aise Johan de
Date:
Type:
Theses
Degree:
Ph.D., Columbia University
Department(s):
Mathematics
Persistent URL:
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
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799
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Suggested Citation:
Alice Rizzardo, , On Fourier-Mukai type functors, Columbia University Academic Commons, .

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