Publication Date

2014-07-01

Availability

Open access

Embargo Period

2014-07-01

Degree Type

Dissertation

Degree Name

Doctor of Philosophy (PHD)

Department

Mathematics (Arts and Sciences)

Date of Defense

2014-04-23

First Committee Member

Ludmil Katzarkov

Second Committee Member

Shulim Kaliman

Third Committee Member

Drew Armstrong

Fourth Committee Member

Rafael Nepomechie

Abstract

Historically, the notion of generation time was first introduced by Rouquier, in his approach to Representation Theory. Then Orlov generalized this idea to the notion of Orlov Spectrum, by considering generation times over all possible generators. Later in the work of Ballard, Favero and Katzarkov, it appears that this invariant carries deep geometric information and it is connected to Birational Geometry. In this thesis we will consider in the case of singularity category of type A and this category with restricted generations. After realizing them combinatorially we use the combinatorics to calculate the spectra of them. This is the baby procedure of creating noncommutative base loci. We will introduce the notion of categorical Okounkov body to analyze this categorical base loci and demonstrate on the An example that jump numbers for categorical multiplier ideal sheaves are the Orlov spectra. The connection established above shall lead to an analogy with the classical Hodge theory.

Keywords

Orlov Spectrum; Categorical Base Locus

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