Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration - Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas

Blick ins Buch

Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration (eBook)

Alfonso Zamora Saiz, Ronald A. Zúñiga-Rojas (Autoren)

eBook Download: PDF

2021 | 1st ed. 2021
XIII, 127 Seiten
Springer International Publishing (Verlag)
978-3-030-67829-6 (ISBN)

Lese- und Medienproben

Ebook-Leseprobe (PDF)

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.

Alfonso Zamora Saiz is a Professor at the School of Computer Science Engineering, Technical University of Madrid, Spain. Holding a PhD in algebraic geometry from the Complutense University of Madrid (2013), he has been a visiting PhD student at Cambridge University and Columbia University, a postdoc at the IST in Lisbon, Lecturer at the California State University Channel Islands and a Professor at the CEU San Pablo University in Madrid. His research interests include algebra, geometry and topology in pure mathematics, as well as data analytical applications and mathematics education.

Ronald A. Zúñiga-Rojas is a Professor at the School of Mathematics, University of Costa Rica (UCR), and is currently a member of both Center of Mathematical and Meta-Mathematical Research (CIMM-UCR) and the Center of Pure and Applied Mathematics Research (CIMPA-UCR). He completed the Doctor's Degree in Mathematics at University of Porto, Portugal, in 2015, in a PhD Program in association with the University of Coimbra in Portugal. His research interests lay on pure mathematics, focused on algebraic geometry, algebraic topology, and differential geometry.

Erscheint lt. Verlag	24.3.2021
Reihe/Serie	SpringerBriefs in Mathematics
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	XIII, 127 p. 16 illus., 12 illus. in color.
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik
Themenwelt	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Algebraic Geometry • Geometric invariant theory • Git • Harder-Narasimham filtration • Higgs bundles • moduli space • Vector Bundles
ISBN-10	3-030-67829-6 / 3030678296
ISBN-13	978-3-030-67829-6 / 9783030678296

Haben Sie eine Frage zum Produkt?

PDF (Wasserzeichen)
Größe: 2,2 MB

DRM: Digitales Wasserzeichen
Dieses eBook enthält ein digitales Wasserzeichen und ist damit für Sie personalisiert. Bei einer missbräuchlichen Weitergabe des eBooks an Dritte ist eine Rückverfolgung an die Quelle möglich.

Dateiformat: PDF (Portable Document Format)
Mit einem festen Seitenlayout eignet sich die PDF besonders für Fachbücher mit Spalten, Tabellen und Abbildungen. Eine PDF kann auf fast allen Geräten angezeigt werden, ist aber für kleine Displays (Smartphone, eReader) nur eingeschränkt geeignet.

Systemvoraussetzungen:
PC/Mac: Mit einem PC oder Mac können Sie dieses eBook lesen. Sie benötigen dafür einen PDF-Viewer - z.B. den Adobe Reader oder Adobe Digital Editions.
eReader: Dieses eBook kann mit (fast) allen eBook-Readern gelesen werden. Mit dem amazon-Kindle ist es aber nicht kompatibel.
Smartphone/Tablet: Egal ob Apple oder Android, dieses eBook können Sie lesen. Sie benötigen dafür einen PDF-Viewer - z.B. die kostenlose Adobe Digital Editions-App.

Buying eBooks from abroad
For tax law reasons we can sell eBooks just within Germany and Switzerland. Regrettably we cannot fulfill eBook-orders from other countries.

Print-Ausgabe

Buch | Softcover

69,54 €