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Geometric invariant theory, holomorp...

Zamora Saiz, Alfonso.

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Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration/ by Alfonso Zamora Saiz, Ronald A. Zuniga-Rojas.
Author:	Zamora Saiz, Alfonso.
other author:	Zuniga-Rojas, Ronald A.
Published:	Cham :Springer International Publishing : : 2021.,
Description:	xiii, 127 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Preface -- Introduction -- Preliminaries -- Geometric Invariant Theory -- Moduli Space of Vector Bundles -- Unstability Correspondence -- Stratifications on the Moduli Space of Higgs Bundles -- References -- Index.
Contained By:	Springer Nature eBook
Subject:	Invariants. -
Online resource:	https://doi.org/10.1007/978-3-030-67829-6
ISBN:	9783030678296

Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration
Zamora Saiz, Alfonso.

Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration[electronic resource] /by Alfonso Zamora Saiz, Ronald A. Zuniga-Rojas. - Cham :Springer International Publishing :2021. - xiii, 127 p. :ill. (some col.), digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

Preface -- Introduction -- Preliminaries -- Geometric Invariant Theory -- Moduli Space of Vector Bundles -- Unstability Correspondence -- Stratifications on the Moduli Space of Higgs Bundles -- References -- Index.

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.

ISBN: 9783030678296

Standard No.: 10.1007/978-3-030-67829-6doiSubjects--Topical Terms:

555710
Invariants.

LC Class. No.: QA201

Dewey Class. No.: 512.5

Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration
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245 1 0 $a Geometric invariant theory, holomorphic vector bundles and the Harder-Narasimhan filtration $h [electronic resource] / $c by Alfonso Zamora Saiz, Ronald A. Zuniga-Rojas.
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300 $a xiii, 127 p. : $b ill. (some col.), digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a Preface -- Introduction -- Preliminaries -- Geometric Invariant Theory -- Moduli Space of Vector Bundles -- Unstability Correspondence -- Stratifications on the Moduli Space of Higgs Bundles -- References -- Index.
520 $a 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.
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