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Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration / / Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas
| Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration / / Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas |
| Autore | Zamora Saiz Alfonso |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (xiii, 127 pages) : illustrations |
| Disciplina | 516.35 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Geometry, Algebraic
Moduli theory Invariants Geometria algebraica Teoria de mòduls |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-67829-6 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 2 Preliminaries -- 2.1 Algebraic Varieties and Groups -- 2.1.1 Algebraic Varieties -- 2.1.2 Group Actions -- 2.2 Sheaf Theory and Schemes -- 2.2.1 Sheaves and Cohomology -- 2.2.2 Schemes -- 2.3 Holomorphic Vector Bundles -- 2.3.1 Vector Bundles -- 2.3.2 Line Bundles -- 2.3.3 Divisors -- 3 Geometric Invariant Theory -- 3.1 Quotients and the Notion of Stability -- 3.2 Hilbert-Mumford Criterion -- 3.3 Symplectic Stability -- 3.4 Examples -- 3.5 Maximal Unstability -- 4 Moduli Space of Vector Bundles -- 4.1 GIT Construction of the Moduli Space -- 4.2 Harder-Narasimhan Filtration -- 4.3 Other Constructions of the Moduli Space of Vector Bundles -- 4.3.1 Analytical Construction of the Moduli Space of Vector Bundles -- 4.3.2 Moduli Space of Representations of the Fundamental Group -- 4.4 Moduli Space of Higgs Bundles -- 4.4.1 Hitchin's Construction -- 4.4.2 Higher Rank and Dimensional Higgs Bundles -- 5 Unstability Correspondence -- 5.1 Correspondence for Vector Bundles -- 5.1.1 Main Correspondence: Holomorphic Vector Bundles -- 5.1.2 Other Correspondences for Augmented Bundles -- 5.2 Quiver Representations -- 5.3 (G,h)-Constellations -- 6 Stratifications on the Moduli Space of Higgs Bundles -- 6.1 Shatz Stratification -- 6.2 C-Action and Białynicki-Birula Stratification -- 6.3 Stratifications in Rank Three -- 6.3.1 Sketch of the Proof of Theorem 6.1 -- 6.3.2 Relationship Between Shatz and Biłynicki-Birula Stratifications for Rank Three Higgs Bundles -- 6.4 Homotopy Groups -- References -- Index. |
| Record Nr. | UNINA-9910483216103321 |
Zamora Saiz Alfonso
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration / / Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas
| Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration / / Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas |
| Autore | Zamora Saiz Alfonso |
| Pubbl/distr/stampa | Cham, Switzerland : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (xiii, 127 pages) : illustrations |
| Disciplina | 516.35 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Geometry, Algebraic
Moduli theory Invariants Geometria algebraica Teoria de mòduls |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 3-030-67829-6 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Intro -- Preface -- Contents -- List of Symbols -- 1 Introduction -- 2 Preliminaries -- 2.1 Algebraic Varieties and Groups -- 2.1.1 Algebraic Varieties -- 2.1.2 Group Actions -- 2.2 Sheaf Theory and Schemes -- 2.2.1 Sheaves and Cohomology -- 2.2.2 Schemes -- 2.3 Holomorphic Vector Bundles -- 2.3.1 Vector Bundles -- 2.3.2 Line Bundles -- 2.3.3 Divisors -- 3 Geometric Invariant Theory -- 3.1 Quotients and the Notion of Stability -- 3.2 Hilbert-Mumford Criterion -- 3.3 Symplectic Stability -- 3.4 Examples -- 3.5 Maximal Unstability -- 4 Moduli Space of Vector Bundles -- 4.1 GIT Construction of the Moduli Space -- 4.2 Harder-Narasimhan Filtration -- 4.3 Other Constructions of the Moduli Space of Vector Bundles -- 4.3.1 Analytical Construction of the Moduli Space of Vector Bundles -- 4.3.2 Moduli Space of Representations of the Fundamental Group -- 4.4 Moduli Space of Higgs Bundles -- 4.4.1 Hitchin's Construction -- 4.4.2 Higher Rank and Dimensional Higgs Bundles -- 5 Unstability Correspondence -- 5.1 Correspondence for Vector Bundles -- 5.1.1 Main Correspondence: Holomorphic Vector Bundles -- 5.1.2 Other Correspondences for Augmented Bundles -- 5.2 Quiver Representations -- 5.3 (G,h)-Constellations -- 6 Stratifications on the Moduli Space of Higgs Bundles -- 6.1 Shatz Stratification -- 6.2 C-Action and Białynicki-Birula Stratification -- 6.3 Stratifications in Rank Three -- 6.3.1 Sketch of the Proof of Theorem 6.1 -- 6.3.2 Relationship Between Shatz and Biłynicki-Birula Stratifications for Rank Three Higgs Bundles -- 6.4 Homotopy Groups -- References -- Index. |
| Record Nr. | UNISA-996466560403316 |
|
Zamora Saiz Alfonso
|
||
| Cham, Switzerland : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
An Introduction to Data Analysis in R [[electronic resource] ] : Hands-on Coding, Data Mining, Visualization and Statistics from Scratch / / by Alfonso Zamora Saiz, Carlos Quesada González, Lluís Hurtado Gil, Diego Mondéjar Ruiz
| An Introduction to Data Analysis in R [[electronic resource] ] : Hands-on Coding, Data Mining, Visualization and Statistics from Scratch / / by Alfonso Zamora Saiz, Carlos Quesada González, Lluís Hurtado Gil, Diego Mondéjar Ruiz |
| Autore | Zamora Saiz Alfonso |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (XV, 276 p. 99 illus., 81 illus. in color.) |
| Disciplina | 519.5 |
| Collana | Use R! |
| Soggetto topico |
Statistics
Big data Data mining R (Computer program language) Statistics and Computing/Statistics Programs Big Data/Analytics Data Mining and Knowledge Discovery Statistics for Business, Management, Economics, Finance, Insurance |
| ISBN | 3-030-48997-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1 Introduction -- 2 Introduction to R -- 3 Databases in R -- 4 Visualization -- 5 Data Analysis with R -- R Packages and Funtions. |
| Record Nr. | UNISA-996418263503316 |
|
Zamora Saiz Alfonso
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
An Introduction to Data Analysis in R : Hands-on Coding, Data Mining, Visualization and Statistics from Scratch / / by Alfonso Zamora Saiz, Carlos Quesada González, Lluís Hurtado Gil, Diego Mondéjar Ruiz
| An Introduction to Data Analysis in R : Hands-on Coding, Data Mining, Visualization and Statistics from Scratch / / by Alfonso Zamora Saiz, Carlos Quesada González, Lluís Hurtado Gil, Diego Mondéjar Ruiz |
| Autore | Zamora Saiz Alfonso |
| Edizione | [1st ed. 2020.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 |
| Descrizione fisica | 1 online resource (XV, 276 p. 99 illus., 81 illus. in color.) |
| Disciplina |
519.5
519.50285 |
| Collana | Use R! |
| Soggetto topico |
Statistics
Big data Data mining R (Computer program language) Statistics and Computing/Statistics Programs Big Data/Analytics Data Mining and Knowledge Discovery Statistics for Business, Management, Economics, Finance, Insurance |
| ISBN | 3-030-48997-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1 Introduction -- 2 Introduction to R -- 3 Databases in R -- 4 Visualization -- 5 Data Analysis with R -- R Packages and Funtions. |
| Record Nr. | UNINA-9910484916903321 |
|
Zamora Saiz Alfonso
|
||
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||