Thesis (Ph. D.)--Duke University, 2007. / Includes bibliographical references.

Thesis (doctoral)--Rheinischen Friedrich-Wilhelm Universität, Bonn, 1981. / Bibliography: p. 78-87.

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1995. / Includes bibliographical references (p. 138-142).

Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 1990. / Includes bibliographical references (p. 114.

Orientador: Marcos Benevenuto Jardim / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-24T09:35:57Z (GMT). No. of bitstreams: 1 GonzalesGargate_MichaelSantos_D.pdf: 3866863 bytes, checksum: 1c42833ca2903ade2f3da9409a389b93 (MD5) Previous issue date: 2014 / Resumo: Nesta tese estudamos o conjunto singular de feixes instanton sobre o espaco projetivo P^3. Um dos resultados principais mostra que o conjunto singular de um feixe instanton não localmente livre de posto 2 tem dimensão pura 1, e que o duplo dual E** e um feixe instanton localmente livre (Teorema 3.1.5). Ambos enunciados são falsos quando o posto de E e maior que 2. Também consideramos os feixes S_E = Ext^1(E;O_P^3) e Q_E = E**/E. Se E e feixe instanton não localmente livre de posto 2 em P3, mostramos que S_E e Q_E sâo feixes instanton de posto 0, conforme de nicão introduzida por Hauzer e Langer em [10]. Alem disso, mostramos que S_E e Q_E são suportados no conjunto singular Sing(E) e possuem o mesmo polinômio de Hilbert (Seções 3.1.2 e 3.1.3). Finalmente, apresentamos algumas propriedades do conjunto singular. Garantimos que o conjunto singular esta contido em uma curva de interseção completa de grau c^2, onde c = c_2(E) e chamada a carga de E (Proposição 3.2.1). Por outro lado, baseado na noção de transformações elementares para instantons dada por Jardim, Markushevich e Tikhomirov em [16], constuímos um exemplo de feixe instanton de posto 2 cujo conjunto conjunto singular não e conexo (Seção 3.2.3). Fornecemos tambem exemplos de feixes instantons de posto 3 cujo conjunto singular consiste de um ponto, e um ponto e uma reta / Abstract: In this thesis we study the singular locus of instanton sheaves on the projective space P^3. We prove that the singular locus Sing(E) of a non-locally free instanton sheaf E of rank 2 has pure dimension 1, and that the double dual E** is a locally free instanton sheaf (Theorem 3.1.5). Both statements are false if the rank of E is larger than 2. We also consider the sheaves S_E = Ext^1(E;OP3) and Q_E = E**/E. When E is a non-locally free instanton sheaf of rank 2, we show that S_E and Q_E are rank 0 instantons, according to a de nition of Hauzer and Langer in [10]. In addition, we show that both are supported the singular locus Sing(E) and have the same Hilbert polynomial (Sections 3.1.2 and 3.1.3). Finally, we present some properties of the singular locus. We guarantee that the singular locus is contained in a complete intersection curve of degree c_2, where c=c_2(E) is called the charge of E (Proposition 3.2.1). Moreover, based on the notion of elementary transformations for instantons given by Jardim, Markushevich and Tikhomirov in [16], we construct an example of a rank 2 instanton sheaf whose singular locus is not connected (Section 3.2.3). We also provide examples of rank 3 instanton sheaves whose singular loci are a single point, and a straight line plus a point / Doutorado / Matematica / Doutor em Matemática

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Tong, Pun Wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 77-78). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.6 / Chapter 2 --- Basic Terminologies --- p.8 / Chapter 3 --- Causality in space-time --- p.12 / Chapter 3.1 --- Preliminaries in space-time --- p.12 / Chapter 3.2 --- Global causality condition --- p.14 / Chapter 3.3 --- Domains of Dependence --- p.23 / Chapter 4 --- Conjugate Points --- p.29 / Chapter 4.1 --- Space of causal curves --- p.29 / Chapter 4.2 --- "Jacobi field, conjugate point and length of geodesic" --- p.35 / Chapter 4.3 --- Congruence of causal geodesics --- p.47 / Chapter 5 --- Singularity Theorems --- p.57 / Chapter 5.1 --- Definition of singularities in space-time --- p.57 / Chapter 5.2 --- A singularity theorem of R. Penrose --- p.60 / Chapter 5.3 --- A singularity theorem of S.W. Hawking and R. Penrose --- p.64 / Appendix --- p.73 / Bibliography --- p.77

Thesis (Ph.D.)--Baylor University, 2007. / Includes bibliographical references (p. 64-66).

Thesis (Ph. D.)--University of Chicago, Dept. of Physics, March 2003. / Includes bibliographical references. Also available on the Internet.

Thesis (doctoral)--Bonn, 1997. / On t.p. x̲ and y̲ are superscript. Includes bibliographical references (p. 117-119).