Lie Methods in Deformation Theory

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Beschreibung

This book furnishes a comprehensive treatment of differential graded Lie algebras, L-infinity algebras, and their use in deformation theory. We believe it is the first textbook devoted to this subject, although the first chapters are also covered in other sources with a different perspective.

Deformation theory is an important subject in algebra and algebraic geometry, with an origin that dates back to Kodaira, Spencer, Kuranishi, Gerstenhaber, and Grothendieck. In the last 30 years, a new approach, based on ideas from rational homotopy theory, has made it possible not only to solve long-standing open problems, but also to clarify the general theory and to relate apparently different features. This approach works over a field of characteristic 0, and the central role is played by the notions of differential graded Lie algebra, L-infinity algebra, and Maurer¿Cartan equations.

The book is written keeping in mind graduate students with a basic knowledge of homological algebra and complex algebraic geometry as utilized, for instance, in the book by K. Kodaira, Complex Manifolds and Deformation of Complex Structures. Although the main applications in this book concern deformation theory of complex manifolds, vector bundles, and holomorphic maps, the underlying algebraic theory also applies to a wider class of deformation problems, and it is a prerequisite for anyone interested in derived deformation theory.

Researchers in algebra, algebraic geometry, algebraic topology, deformation theory, and noncommutative geometry are the major targets for the book.

Über den Autor

Professor Marco Manetti was born in 1966. He is full professor of geometry at the Sapienza University of Roma, Italy (since 2001). His research interests involve algebraic geometry, deformation theory, homotopical algebra and higher operations in geometry. He is the author of the book "Topologia", Springer UTX (2008).

Zusammenfassung

Introduces differential graded Lie algebras, L-infinity algebras, and their homotopy classification in detail

Applies the differential graded Lie approach to deformation theory of complex manifolds-the first book to do so

Includes practice exercises at the end of every chapter

Inhaltsverzeichnis

1. An Overview of Deformation Theory of Complex Manifolds.- 2. Lie Algebras.- 3. Functors of Artin Rings.- 4. Infinitesimal Deformations of Complex Manifolds and Vector Bundles.- 5. Differential Graded Lie Algebras.- 6. Maurer-Cartan Equation and Deligne Groupoids.- 7. Totalization and Descent of Deligne Groupoids.- 8. Deformations of Complex Manifolds and Holomorphic Maps.- 9. Poisson, Gerstenhaber and Batalin-Vilkovisky Algebras.- 10. L1-algebras.- 11. Coalgebras and Coderivations.- 12. L1-morphisms.- 13. Formal Kuranishi Families and Period Maps.- References.

Details

Erscheinungsjahr:	2022
Fachbereich:	Arithmetik & Algebra
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Reihe:	Springer Monographs in Mathematics
Inhalt:	xii 574 S. 23 s/w Illustr. 574 p. 23 illus.
ISBN-13:	9789811911842
ISBN-10:	9811911843
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Manetti, Marco
Auflage:	1st ed. 2022
Hersteller:	Springer Singapore Springer Nature Singapore Springer Monographs in Mathematics
Maße:	241 x 160 x 37 mm
Von/Mit:	Marco Manetti
Erscheinungsdatum:	02.08.2022
Gewicht:	1,039 kg

Artikel-ID: 121194616