On Fourier-Mukai type functors
type: CreativeWork
description: 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.
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.
author: Rizzardo, Alice
language: English
keywords: Mathematics, Functor theory, Algebra, Homological, Isomorphisms (Mathematics)
date published: 2012
date modified: 2026-07-24T01:44:18Z
provider: Columbia University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Columbia University

PropertyValue
property ID: DOI
value: 10.7916/D8639WTV