Oberwolfach Seminar: Deformations of Algebraic and Analytic Structures

Date:

October 9th - October 15th, 2005

Organizers:

Ragnar-Olaf Buchweitz, Toronto

Hubert Flenner, Bochum

Programme:

It was Riemann's insight that smooth compact complex curves of fixed genus g depend on 3g-3 complex parameters, which he determined in an elegant and simple manner via coverings of the projective line. Ground breaking work in deformation theory of higher dimensional complex manifolds was done by Kodaira and Spencer in the late 50s of the last century. They introduced the concept of a "versal deformation", which in a certain sense is a local moduli space. In its beginnings, this theory was basically concerned with variations of complex structures on a given complex manifold, and the theory of elliptic differential operators played a central role. Using ideas of Grothendieck, modern deformation theory was soon formalized, and, as a consequence, gained a much wider range of application, e.g., on singularities, vector bundles, and modules.

As a side effect of its formalization, modern deformation theory is difficult to access for the beginner. The seminar aims to give an introduction oriented towards the practical user's needs, so that the methods of deformation theory can become tools for concrete problems in complex analytic and algebraic geometry. Among other things, the following items will be treated: formal deformation theory, versal and semi-universal deformation, criteria for smoothness and unobstructedness of the base space of a versal deformation, determination of the components of the semi-universal deformation, openness of versality, moduli spaces, cotangent complexes. The theory will be presented in connection with application examples such as compact spaces, modules and singularities.

Prerequisites:

Solid knowledge in complex analytic or algebraic geometry, sheaf theory and cohomology theory.

Deadline for applications:

September 1st, 2005

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.