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

Reference week

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