Deformation Theory
MATH-657 / 3 credits
Teacher: Wyss Dimitri Stelio
Language: English
Remark: Registration only to edma@epfl.ch until 31.12.2023
Frequency
Only this year
Summary
We will study classical and modern deformation theory of schemes and coherent sheaves. Participants should have a solid background in scheme-theory, for example being familiar with the first 3 chapters of Hartshorne's 'Algebraic Geometry'.
Content
We will study classical and modern deformation theory of schemes and coherent sheaves. Participants will be assigned a topic, asked to deliver a talk (1 or 2 hour lecture depending on the number of participants) and prepare exercises during the week of February 5th.
Furthermore, the following topics will be addressed:
- Hilbert Schemes
- First order deformations
- Higher order deformations
- Formal moduli of plane curve singularities, coherent sheaves and schemes.
- Global moduli of curves and vector bundles
Keywords
Deformation theory
Learning Outcomes
By the end of the course, the student must be able to:
- Produce a talk
- Plan an exercice session
- Define the important concepts in the deformation theory of schemes and coherent sheaves.
Resources
Bibliography
Deformation theory by Hartshorne
Ressources en bibliothèque
Moodle Link
In the programs
- Number of places: 10
- Exam form: Oral presentation (session free)
- Subject examined: Deformation Theory
- Lecture: 18 Hour(s)
- Exercises: 13 Hour(s)
- Practical work: 35 Hour(s)
- Type: optional