Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration (Record no. 60653)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02235 a2200277 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 241212b2021 |||||||| |||| 001 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| ISBN | 9783030678289 (PB) |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | 512.72/73 |
| Item number | SAI |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Saiz, Alfonso Zamora |
| 245 ## - TITLE STATEMENT | |
| Title | Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher | Springer |
| Year of publication | 2021 |
| Place of publication | Switerland |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | xiii, 127p |
| 440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE | |
| Title | Springer briefs in mathematics |
| 500 ## - GENERAL NOTE | |
| General note | Includes index |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes bibliography (p. 121-124) and references. |
| 505 ## - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1. Introduction<br/>2. Preliminaries<br/>3. Geometric Invariant Theory<br/>4. Moduli Space of Vector Bundles<br/>5. Unstability Correspondence<br/>6. Stratifications on the Moduli Space of Higgs Bundles |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | This book introduces key topics on Geometric Invariant Theory, a technique to obtaining quotients in algebraic geometry with a good set of properties, through various examples. It starts from the classical Hilbert classification of binary forms, advancing to the construction of the moduli space of semistable holomorphic vector bundles, and to Hitchin’s theory on Higgs bundles. The relationship between the notion of stability between algebraic, differential and symplectic geometry settings is also covered. Unstable objects in moduli problems -- a result of the construction of moduli spaces -- get specific attention in this work. The notion of the Harder-Narasimhan filtration as a tool to handle them, and its relationship with GIT quotients, provide instigating new calculations in several problems. Applications include a survey of research results on correspondences between Harder-Narasimhan filtrations with the GIT picture and stratifications of the moduli space of Higgs bundles. Graduate students and researchers who want to approach Geometric Invariant Theory in moduli constructions can greatly benefit from this reading, whose key prerequisites are general courses on algebraic geometry and differential geometry. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Algebraic geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Algebraic varieties |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Geometric varieties |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Vector bundles |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 700 ## - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Zuniga-Rojas, Ronald A. |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | BOOKS |
| Withdrawn status | Lost status | Damaged status | Not for loan | Home library | Current library | Shelving location | Full call number | Accession Number | Koha item type |
|---|---|---|---|---|---|---|---|---|---|
| 1 | IMSc Library | IMSc Library | Technical Processing | 512.72/73 SAI | 78311 | BOOKS |