Moduli spaces of vector bundles on algebraic varieties

[eng] his thesis seeks to contribute to a deeper understanding of the moduli spaces M-sub X, H (r; c1,., Cmin{r;n}) of rank r, H-stable vector bundles E on an n-dimensional variety X, with fixed Chern classes c-sub1(E) = csub1 H-super2i ( X , Z) , displaying new and interesting geometric properties...

ver descrição completa

Detalhes bibliográficos
Autor: Costa Farràs, Laura
Formato: tesis doctoral
Estado:Versión publicada
Fecha de publicación:1998
País:España
Recursos:Universidad de Barcelona
Repositorio:Dipòsit Digital de la UB
OAI Identifier:oai:diposit.ub.edu:2445/35136
Acesso em linha:https://hdl.handle.net/2445/35136
http://www.tdx.cat/TDX-0513108-105915
http://hdl.handle.net/10803/659
Access Level:acceso abierto
Palavra-chave:Geometria algebraica
Teoria de mòduls
Feixos fibrats (Matemàtica)
Algebraic geometry
Moduli theory
Fiber bundles (Mathematics)
id ES_7d78b8e0a3ec35dc548450a748e6bac3
oai_identifier_str oai:diposit.ub.edu:2445/35136
network_acronym_str ES
network_name_str España
repository_id_str
spelling Moduli spaces of vector bundles on algebraic varietiesCosta Farràs, LauraGeometria algebraicaTeoria de mòdulsFeixos fibrats (Matemàtica)Algebraic geometryModuli theoryFiber bundles (Mathematics)[eng] his thesis seeks to contribute to a deeper understanding of the moduli spaces M-sub X, H (r; c1,., Cmin{r;n}) of rank r, H-stable vector bundles E on an n-dimensional variety X, with fixed Chern classes c-sub1(E) = csub1 H-super2i ( X , Z) , displaying new and interesting geometric properties of M-sub X, H (r; c1,., Cmin{r;n}) which nicely reflect the general philosophy that moduli spaces inherit a lot of .geometrical properties of the underlying variety X. More precisely, we consider a smooth, irreducible, n-dimensional, projective variety X defined over an algebraically closed field k of characteristic zero, H an ample divisor on X, r >/2 an integer and c-subi H-super2i(X,Z) for i = 1, .,min{r,n}. We denote by M-sub X, H (r; c1,., Cmin{r;n}) the moduli space of rank r, vector bundles E on X, H-stable, in the sense of Mumford-Takemoto, with fixed Chern classes c-subi(E) = c-subi for i = 1, . , min{r, n}. The contents of this Thesis is the following: Chapter 1 is devoted to provide the reader with the general background that we will need in the sequel. In the first two sections, we have collected the main definitions and results concerning coherent sheaves and moduli spaces, at least, those we will need through this work. The aim of Chapter 2 is to establish the enterions of rationality for moduli spaces of rank two, it-stable vector bundles on a smooth, irreducible, rational surface X that will be used as one of our tools for answering Question (1), who is that follows: "Let X be a smooth, irreducible, rational surface. Fix C-sub1 Pic(X) and 0 « c2 Z. Is there an ample divisor H on X such that M-sub X,H(2; Ci, c2) is rational?" In Chapter 3 we prove that the moduli space M-sub X,H(2; Ci, c2) of rank two, H-stable, vector bundles E on a smooth, irreducible, rational surface X, with fixed Chern classes C-sub1(E) = C-sub1 Pic(X) and 0 « C-sub2«(E) Z is a smooth, irreducible, rational, quasi-projective variety (Theorem 3.3.7) which solves Question (1). In Chapter 4 we study moduli spaces (M-sub X,H(2; Ci, c2)) of rank r, H-stable vector bundles on either minimal rational surfaces or on algebraic K3 surfaces. In Chapter 5 we deal with moduli spaces M-sub x,l (2;Ci,C2) of rank two, L-stable vector bundles E, on P-bundles of arbitrary dimension, with fixed Chern classes.Universitat de BarcelonaMiró-Roig, Rosa M. (Rosa Maria)Universitat de Barcelona. Departament d'Àlgebra i Geometria1998info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://hdl.handle.net/2445/35136http://www.tdx.cat/TDX-0513108-105915http://hdl.handle.net/10803/659Tesis Doctorals - Departament - Algebra i Geometriareponame:Dipòsit Digital de la UBinstname:Universidad de BarcelonaInglés(c) Costa Farràs, 1998info:eu-repo/semantics/openAccessoai:diposit.ub.edu:2445/351362026-05-27T06:46:51Z
dc.title.none.fl_str_mv Moduli spaces of vector bundles on algebraic varieties
title Moduli spaces of vector bundles on algebraic varieties
spellingShingle Moduli spaces of vector bundles on algebraic varieties
Costa Farràs, Laura
Geometria algebraica
Teoria de mòduls
Feixos fibrats (Matemàtica)
Algebraic geometry
Moduli theory
Fiber bundles (Mathematics)
title_short Moduli spaces of vector bundles on algebraic varieties
title_full Moduli spaces of vector bundles on algebraic varieties
title_fullStr Moduli spaces of vector bundles on algebraic varieties
title_full_unstemmed Moduli spaces of vector bundles on algebraic varieties
title_sort Moduli spaces of vector bundles on algebraic varieties
dc.creator.none.fl_str_mv Costa Farràs, Laura
author Costa Farràs, Laura
author_facet Costa Farràs, Laura
author_role author
dc.contributor.none.fl_str_mv Miró-Roig, Rosa M. (Rosa Maria)
Universitat de Barcelona. Departament d'Àlgebra i Geometria
dc.subject.none.fl_str_mv Geometria algebraica
Teoria de mòduls
Feixos fibrats (Matemàtica)
Algebraic geometry
Moduli theory
Fiber bundles (Mathematics)
topic Geometria algebraica
Teoria de mòduls
Feixos fibrats (Matemàtica)
Algebraic geometry
Moduli theory
Fiber bundles (Mathematics)
description [eng] his thesis seeks to contribute to a deeper understanding of the moduli spaces M-sub X, H (r; c1,., Cmin{r;n}) of rank r, H-stable vector bundles E on an n-dimensional variety X, with fixed Chern classes c-sub1(E) = csub1 H-super2i ( X , Z) , displaying new and interesting geometric properties of M-sub X, H (r; c1,., Cmin{r;n}) which nicely reflect the general philosophy that moduli spaces inherit a lot of .geometrical properties of the underlying variety X. More precisely, we consider a smooth, irreducible, n-dimensional, projective variety X defined over an algebraically closed field k of characteristic zero, H an ample divisor on X, r >/2 an integer and c-subi H-super2i(X,Z) for i = 1, .,min{r,n}. We denote by M-sub X, H (r; c1,., Cmin{r;n}) the moduli space of rank r, vector bundles E on X, H-stable, in the sense of Mumford-Takemoto, with fixed Chern classes c-subi(E) = c-subi for i = 1, . , min{r, n}. The contents of this Thesis is the following: Chapter 1 is devoted to provide the reader with the general background that we will need in the sequel. In the first two sections, we have collected the main definitions and results concerning coherent sheaves and moduli spaces, at least, those we will need through this work. The aim of Chapter 2 is to establish the enterions of rationality for moduli spaces of rank two, it-stable vector bundles on a smooth, irreducible, rational surface X that will be used as one of our tools for answering Question (1), who is that follows: "Let X be a smooth, irreducible, rational surface. Fix C-sub1 Pic(X) and 0 « c2 Z. Is there an ample divisor H on X such that M-sub X,H(2; Ci, c2) is rational?" In Chapter 3 we prove that the moduli space M-sub X,H(2; Ci, c2) of rank two, H-stable, vector bundles E on a smooth, irreducible, rational surface X, with fixed Chern classes C-sub1(E) = C-sub1 Pic(X) and 0 « C-sub2«(E) Z is a smooth, irreducible, rational, quasi-projective variety (Theorem 3.3.7) which solves Question (1). In Chapter 4 we study moduli spaces (M-sub X,H(2; Ci, c2)) of rank r, H-stable vector bundles on either minimal rational surfaces or on algebraic K3 surfaces. In Chapter 5 we deal with moduli spaces M-sub x,l (2;Ci,C2) of rank two, L-stable vector bundles E, on P-bundles of arbitrary dimension, with fixed Chern classes.
publishDate 1998
dc.date.none.fl_str_mv 1998
dc.type.none.fl_str_mv info:eu-repo/semantics/doctoralThesis
info:eu-repo/semantics/publishedVersion
format doctoralThesis
status_str publishedVersion
dc.identifier.none.fl_str_mv https://hdl.handle.net/2445/35136
http://www.tdx.cat/TDX-0513108-105915
http://hdl.handle.net/10803/659
url https://hdl.handle.net/2445/35136
http://www.tdx.cat/TDX-0513108-105915
http://hdl.handle.net/10803/659
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.rights.none.fl_str_mv (c) Costa Farràs, 1998
info:eu-repo/semantics/openAccess
rights_invalid_str_mv (c) Costa Farràs, 1998
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universitat de Barcelona
publisher.none.fl_str_mv Universitat de Barcelona
dc.source.none.fl_str_mv Tesis Doctorals - Departament - Algebra i Geometria
reponame:Dipòsit Digital de la UB
instname:Universidad de Barcelona
instname_str Universidad de Barcelona
reponame_str Dipòsit Digital de la UB
collection Dipòsit Digital de la UB
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869411665835982848
score 15.301603

Registos relacionados