Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration write by Alfonso Zamora Saiz. This book was released on 2021-03-24. Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration available in PDF, EPUB and Kindle. 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.
Holomorphic Vector Bundles over Compact Complex Surfaces
Holomorphic Vector Bundles over Compact Complex Surfaces - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Holomorphic Vector Bundles over Compact Complex Surfaces write by Vasile Brinzanescu. This book was released on 2006-11-14. Holomorphic Vector Bundles over Compact Complex Surfaces available in PDF, EPUB and Kindle. The purpose of this book is to present the available (sometimes only partial) solutions to the two fundamental problems: the existence problem and the classification problem for holomorphic structures in a given topological vector bundle over a compact complex surface. Special features of the nonalgebraic surfaces case, like irreducible vector bundles and stability with respect to a Gauduchon metric, are considered. The reader requires a grounding in geometry at graduate student level. The book will be of interest to graduate students and researchers in complex, algebraic and differential geometry.
Algebraic Surfaces and Holomorphic Vector Bundles
Algebraic Surfaces and Holomorphic Vector Bundles - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Surfaces and Holomorphic Vector Bundles write by Robert Friedman. This book was released on 2012-12-06. Algebraic Surfaces and Holomorphic Vector Bundles available in PDF, EPUB and Kindle. A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
Geometric Invariant Theory
Geometric Invariant Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Invariant Theory write by David Mumford. This book was released on 1994. Geometric Invariant Theory available in PDF, EPUB and Kindle. "Geometric Invariant Theory" by Mumford/Fogarty (the firstedition was published in 1965, a second, enlarged editonappeared in 1982) is the standard reference on applicationsof invariant theory to the construction of moduli spaces.This third, revised edition has been long awaited for by themathematical community. It is now appearing in a completelyupdated and enlarged version with an additional chapter onthe moment map by Prof. Frances Kirwan (Oxford) and a fullyupdated bibliography of work in this area.The book deals firstly with actions of algebraic groups onalgebraic varieties, separating orbits by invariants andconstructionquotient spaces; and secondly with applicationsof this theory to the construction of moduli spaces.It is a systematic exposition of the geometric aspects ofthe classical theory of polynomial invariants.
The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds
The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds write by Martin Lübke. This book was released on 2006. The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds available in PDF, EPUB and Kindle. We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds, and we discuss differential geometric properties of the corresponding moduli spaces. This correspondence refers to moduli spaces of ``universal holomorphic oriented pairs''. Most of the classical moduli problems in complex geometry (e. g. holomorphic bundles with reductive structure groups, holomorphic pairs, holomorphic Higgs pairs, Witten triples, arbitrary quiver moduli problems) are special cases of this universal classification problem. Our Kobayashi-Hitchin correspondence relates the complex geometric concept ``polystable oriented holomorphic pair'' to the existence of a reduction solving a generalized Hermitian-Einstein equation. The proof is based on the Uhlenbeck-Yau continuity method. Using ideas from Donaldson theory, we further introduce and investigate canonical Hermitian metrics on such moduli spaces. We discuss in detail remarkable classes of moduli spaces in the non-Kahlerian framework: Oriented holomorphic structures, Quot-spaces, oriented holomorphic pairs and oriented vortices, non-abelian Seiberg-Witten monopoles.
