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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
|
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| 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 | ||
| ||
Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method / / Toshiki Mabuchi
| Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method / / Toshiki Mabuchi |
| Autore | Mabuchi Toshiki <1950-> |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (x, 128 pages) : illustrations |
| Disciplina | 516.36 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Geometry, Differential
Manifolds (Mathematics) Moduli theory Geometria diferencial Varietats (Matemàtica) Teoria de mòduls |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-0500-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Preliminaries -- 1.2 The Deligne Pairings with Metrics -- 1.3 Definition of the Chow Norm -- 1.4 The First and Second Variation Formulas for the Chow Norm -- Problems -- 2 The Donaldson-Futaki Invariant -- 2.1 Test Configurations -- 2.2 Test Configurations Associated to One-Parameter Groups -- 2.3 Definition of the Donaldson-Futaki Invariant -- 2.4 Expression of DF1 as an Intersection Number -- 2.5 The Relationship Between the Chow Norm and DFi -- Problems -- 3 Canonical Kähler Metrics -- 3.1 Canonical Kähler Metrics on Compact Complex Manifolds -- 3.2 Conformal Changes of Metrics by Hamiltonian Functions -- Problems -- 4 Norms for Test Configurations -- 4.1 Norms for Test Configurations of a Fixed Exponent -- 4.2 The Asymptotic 1-norm of a Test Configuration -- 4.3 Relative Norms for Test Configurations -- 4.4 The Twisted Kodaira Embedding -- 4.5 The Donaldson-Futaki Invariant for Sequences -- Problems -- 5 Stabilities for Polarized Algebraic Manifolds -- 5.1 The Chow Stability -- 5.2 The Hilbert Stability -- 5.3 K-stability -- 5.4 Relative Stability -- Problems -- 6 The Yau-Tian-Donaldson Conjecture -- 6.1 The Calabi Conjecture -- 6.2 The Yau-Tian-Donaldson Conjecture -- 6.3 The K-Energy -- 6.4 Extremal Kähler Versions of the Conjecture -- Problems -- 7 Stability Theorem -- 7.1 Strong K-Semistability of CSC Kähler Manifolds -- 7.2 Relative Balanced Metrics -- 7.3 Strong Relative K-Semistability of Extremal Kähler Manifolds -- 7.4 K-Polystability of Extremal Kähler Manifolds -- 7.5 A Reformulation of the Definition of the Invariant F ({μj}) -- Problems -- 8 Existence Problem -- 8.1 A Result of He on the Existence of Extremal Kähler Metrics -- 8.2 Some Observations on the Existence Problem -- Problems -- 9 Canonical Kähler Metrics on Fano Manifolds -- 9.1 Kähler Metrics in Anticanonical Class.
9.2 Extremal Vector Fields -- 9.3 An Obstruction of Matsushima's Type -- 9.4 An Invariant as an Obstruction to the Existence -- 9.5 Examples of Generalized Kähler-Einstein Metrics -- 9.6 Extremal Metrics on Generalized Kähler-Einstein Manifolds -- 9.7 The Product Formula for the Invariant γX -- 9.8 Yao's Result for Toric Fano Manifolds -- 9.9 Hisamoto's Result on the Existence Problem -- Problems -- A Geometry of Pseudo-Normed Graded Algebras -- A.1 Differential Geometric Viewpoints -- A.2 Lp-Spaces -- A.3 An Orthogonal Direct Sum of Lp-Spaces -- A.4 A Boundedness Theorem for Lp-Spaces -- A.5 The Moduli Space of Lp-Spaces -- A.6 A Multiplicative System of Lp-Spaces -- A.7 Degeneration Phenomena -- Solutions -- Problems of Chap.1 -- Problems of Chap.2 -- Problems of Chap.3 -- Problems of Chap.4 -- Problems of Chap.5 -- Problems of Chap.6 -- Problems of Chap.7 -- Problems of Chap.8 -- Problems of Chap.9 -- Bibliography. |
| Record Nr. | UNINA-9910484266903321 |
|
Mabuchi Toshiki <1950->
|
||
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method / / Toshiki Mabuchi
| Test configurations, stabilities and canonical Kähler metrics : complex geometry by the energy method / / Toshiki Mabuchi |
| Autore | Mabuchi Toshiki <1950-> |
| Pubbl/distr/stampa | Singapore : , : Springer, , [2021] |
| Descrizione fisica | 1 online resource (x, 128 pages) : illustrations |
| Disciplina | 516.36 |
| Collana | SpringerBriefs in Mathematics |
| Soggetto topico |
Geometry, Differential
Manifolds (Mathematics) Moduli theory Geometria diferencial Varietats (Matemàtica) Teoria de mòduls |
| Soggetto genere / forma | Llibres electrònics |
| ISBN | 981-16-0500-9 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Introduction -- 1.1 Preliminaries -- 1.2 The Deligne Pairings with Metrics -- 1.3 Definition of the Chow Norm -- 1.4 The First and Second Variation Formulas for the Chow Norm -- Problems -- 2 The Donaldson-Futaki Invariant -- 2.1 Test Configurations -- 2.2 Test Configurations Associated to One-Parameter Groups -- 2.3 Definition of the Donaldson-Futaki Invariant -- 2.4 Expression of DF1 as an Intersection Number -- 2.5 The Relationship Between the Chow Norm and DFi -- Problems -- 3 Canonical Kähler Metrics -- 3.1 Canonical Kähler Metrics on Compact Complex Manifolds -- 3.2 Conformal Changes of Metrics by Hamiltonian Functions -- Problems -- 4 Norms for Test Configurations -- 4.1 Norms for Test Configurations of a Fixed Exponent -- 4.2 The Asymptotic 1-norm of a Test Configuration -- 4.3 Relative Norms for Test Configurations -- 4.4 The Twisted Kodaira Embedding -- 4.5 The Donaldson-Futaki Invariant for Sequences -- Problems -- 5 Stabilities for Polarized Algebraic Manifolds -- 5.1 The Chow Stability -- 5.2 The Hilbert Stability -- 5.3 K-stability -- 5.4 Relative Stability -- Problems -- 6 The Yau-Tian-Donaldson Conjecture -- 6.1 The Calabi Conjecture -- 6.2 The Yau-Tian-Donaldson Conjecture -- 6.3 The K-Energy -- 6.4 Extremal Kähler Versions of the Conjecture -- Problems -- 7 Stability Theorem -- 7.1 Strong K-Semistability of CSC Kähler Manifolds -- 7.2 Relative Balanced Metrics -- 7.3 Strong Relative K-Semistability of Extremal Kähler Manifolds -- 7.4 K-Polystability of Extremal Kähler Manifolds -- 7.5 A Reformulation of the Definition of the Invariant F ({μj}) -- Problems -- 8 Existence Problem -- 8.1 A Result of He on the Existence of Extremal Kähler Metrics -- 8.2 Some Observations on the Existence Problem -- Problems -- 9 Canonical Kähler Metrics on Fano Manifolds -- 9.1 Kähler Metrics in Anticanonical Class.
9.2 Extremal Vector Fields -- 9.3 An Obstruction of Matsushima's Type -- 9.4 An Invariant as an Obstruction to the Existence -- 9.5 Examples of Generalized Kähler-Einstein Metrics -- 9.6 Extremal Metrics on Generalized Kähler-Einstein Manifolds -- 9.7 The Product Formula for the Invariant γX -- 9.8 Yao's Result for Toric Fano Manifolds -- 9.9 Hisamoto's Result on the Existence Problem -- Problems -- A Geometry of Pseudo-Normed Graded Algebras -- A.1 Differential Geometric Viewpoints -- A.2 Lp-Spaces -- A.3 An Orthogonal Direct Sum of Lp-Spaces -- A.4 A Boundedness Theorem for Lp-Spaces -- A.5 The Moduli Space of Lp-Spaces -- A.6 A Multiplicative System of Lp-Spaces -- A.7 Degeneration Phenomena -- Solutions -- Problems of Chap.1 -- Problems of Chap.2 -- Problems of Chap.3 -- Problems of Chap.4 -- Problems of Chap.5 -- Problems of Chap.6 -- Problems of Chap.7 -- Problems of Chap.8 -- Problems of Chap.9 -- Bibliography. |
| Record Nr. | UNISA-996466550003316 |
|
Mabuchi Toshiki <1950->
|
||
| Singapore : , : Springer, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
