Conducted in
term:
2024Z
Erasmus code: 11.1
ISCED code: 0541
ECTS credits:
6
Language:
English
Organized by:
Faculty of Mathematics, Informatics, and Mechanics
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.
Course coordinators
Type of course
elective monographs
Mode
Self-reading
Requirements
Prerequisites (description)
Good knowledge of algebraic geometry, say, at the level of Vakil's "Foundation of algebraic geometry" book, up to chapter 9 or 13.
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.