Lie Methods in Deformation Theory

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).

“The book is very clearly written and nicely structured with abstract, algebraic parts, followed by concrete applications that make it very suitable as a base for courses either in the general theory of deformation of complex manifolds or to various special aspects.” (Andrei D. Halanay, Mathematical Reviews, September, 2023)“This book provides an accessible and self-contained approach to the field through the particular lens of Lie theoretical techniques. ... The book is introductory in its nature. ... The book is wonderfully well-written and it is always balanced. ... the book is also full of fun and relevant exercises, and the proofs are clear and concise when possible ... . The more abstract chapters are balanced out too by a wealth of examples to read along … .” (Camilo Andres Angulo Santacruz, zbMATH 1509.14001, 2023)

• 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.