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Compactifying Moduli Spaces (Advanced Courses in Mathematics - CRM Barcelona)

De (autor) , , Editat de Gilberto Bini, Martí Lahoz, Emanuele Macrí, Paolo Stellari
Notă GoodReads:
en Limba Engleză Carte Paperback – 12 Feb 2016
This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated.
Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps.
Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.
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Specificații

ISBN-13: 9783034809207
ISBN-10: 3034809204
Pagini: 150
Ilustrații: Bibliographie
Dimensiuni: 168 x 240 x 11 mm
Greutate: 2.54 kg
Ediția: 1st ed. 2016
Editura: Springer
Colecția Birkhäuser
Seria Advanced Courses in Mathematics - CRM Barcelona

Locul publicării: Basel, Switzerland

Public țintă

Graduate

Cuprins

Foreword.- 1: Perspectives on moduli spaces.- The GIT Approach to constructing moduli spaces.- Moduli and periods.- The KSBA approach to moduli spaces.- Bibliography.- 2: Compact moduli of surfaces and vector bundles.- Moduli spaces of surfaces of general type.- Wahl singularities.- Examples of degenerations of Wahl type.- Exceptional vector bundles associated to Wahl degenerations.- Examples.- Bibliography.- 3: Notes on the moduli space of stable quotients.- Morphism spaces and Quot schemes over a fixed curve.- Stable quotients.- Stable quotient invariants.- Wall-crossing and other geometries.- Bibliography.

Textul de pe ultima copertă

This book focusses on a large class of objects in moduli theory and provides different perspectives from which compactifications of moduli spaces may be investigated.
Three contributions give an insight on particular aspects of moduli problems. In the first of them, various ways to construct and compactify moduli spaces are presented. In the second, some questions on the boundary of moduli spaces of surfaces are addressed. Finally, the theory of stable quotients is explained, which yields meaningful compactifications of moduli spaces of maps.
Both advanced graduate students and researchers in algebraic geometry will find this book a valuable read.

Caracteristici

Provides an overview of main techniques in compactifying moduli spaces
Shows various approaches to find degenerations of family of smooth manifolds
Develops various examples which help understanding the theory involved