Deformation theory and moduli spaces 1000-1M19DPM
Briefly:
(1) Deformation problems: examples and local theory.
(2) Moduli spaces: Grassmannians, Hilbert and perhaps Quot schemes.
(3) Applications of homological algebra to understanding the local structure of the deformation spaces.
(4) Further directions: beyond schemes.
Type of course
Mode
Requirements
Prerequisites (description)
Course coordinators
Learning outcomes
The student understand the main concepts of the theory and is able to apply them to understand geometric or algebraic problems.
Assessment criteria
Exam (80%), exercises (20%).
Bibliography
"Deformation Theory", R. Hartshorne,
"The geometry of schemes", D. Eisenbud, J. Harris,
"Deformations of Algebraic Schemes", E. Sernesi,
Fundamental Algebraic Geometry explained, Fantechi et.al.
Foundations of Algebraic Geometry, Vakil.
Additional information
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