Deformation Theory (Wintersemester 2015)


2 Stunden pro Woche, Dienstag 15-17 Uhr, RUD 25, 2.006.

Organiser: Michael Kemeny



"Any area of mathematics is a kind of deformation theory.'' Kontsevich-Soibelman, rephrasing I. Gelfand.

A central concept in modern mathematics is the notion of the "moduli space" parametrising all mathematical objects of a given kind. Deformation theory is then the local study of this moduli space. In this seminar (which will function largely as a lecture series), we aim to define what a moduli space is and give dimension bounds on this space as well as criteria for when it is smooth.

As well as developing the general theory, we will discuss many examples from algebra (deformations of rings, algebras and Lie algebras), complex analysis (deformations of complex manifolds, deformations of analytic singularity types) and algebraic geometry (curves, morphisms).


Prerequisites: basic knowledge of projective varieties and sheaf cohomology will be assumed (at the level of Hartshorne).
Course Outline / Inhaltsbeschreibung: pdf file
     *PLEASE NOTE, THERE WILL BE NO LECTURE ON 2.02.16*
Lecture Notes:
Lectures 1+2: pdf file
Lecture 3: Handwritten : pdf file      Typed- Thanks Emre! : pdf file
Lecture 4: Handwritten: pdf file      Typed : pdf file
Lecture 5: Handwritten: pdf file      Typed : pdf file
Lecture 6: Handwritten: pdf file      Typed : pdf file
Lecture 7: Handwritten: pdf file      Typed : pdf file
Lecture 8: Handwritten: pdf file      Typed : pdf file
Lecture 9: Handwritten: pdf file      Typed : pdf file
Lecture 10: Handwritten: pdf file      Typed : pdf file
Lecture 11: Handwritten: pdf file
Lecture 12: Handwritten: pdf file
References: some references we plan to use include
  • "Introduction to Singularities and Deformations", G.M. Greuel, C. Lossen, E. Shustin
  • "Deformations of Algebraic Schemes", E. Sernesi
  • "Deformation Theory", R. Hartshorne

    schlessinger
    Michael Schlessinger, copyright George M. Bergman