Geometric Invariant Theory Holomorphic Vector Bundles and the Harder Narasimhan Filtration is popular PDF and ePub book, written by Alfonso Zamora Saiz in 2021-03-24, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Geometric Invariant Theory Holomorphic Vector Bundles and the Harder Narasimhan Filtration can be Read Online from any device for your convenience.
Geometric Invariant Theory Holomorphic Vector Bundles and the Harder Narasimhan Filtration Book PDF Summary
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.
Detail Book of Geometric Invariant Theory Holomorphic Vector Bundles and the Harder Narasimhan Filtration PDF
- Author : Alfonso Zamora Saiz
- Release : 24 March 2021
- Publisher : Springer Nature
- ISBN : 9783030678296
- Genre : Mathematics
- Total Page : 127 pages
- Language : English
- PDF File Size : 14,5 Mb
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