SpringerBriefs in Mathematics

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

Authors: Zamora Saiz, Alfonso, Zúñiga-Rojas, Ronald A.

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  • Introduces key topics on Geometric Invariant Theory through examples and applications
  • Covers Hilbert classification of binary forms and Hitchin's theory on Higgs bundles
  • Takes particular note of unstable objects in module problems
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eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-030-67829-6
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  • Included format: EPUB, PDF
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  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-030-67828-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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About this book

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.

About the authors

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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook 42,79 €
price for Spain (gross)
  • ISBN 978-3-030-67829-6
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 51,99 €
price for Spain (gross)
  • ISBN 978-3-030-67828-9
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive license to Springer Nature Switzerland AG
eBook ISBN
978-3-030-67829-6
DOI
10.1007/978-3-030-67829-6
Softcover ISBN
978-3-030-67828-9
Series ISSN
2191-8198
Edition Number
1
Number of Pages
XIII, 127
Number of Illustrations
4 b/w illustrations, 12 illustrations in colour
Topics