University of Sydney
School of Mathematics and Statistics
11:-12:30
in Carslaw 709 on Wednesday 9 May.
Ben Martin
Moduli spaces
Let A be a collection of geometric objects (e.g. all vector bundles over a
fixed surface), let ~ be an equivalence relation on A (e.g. isomorphism
of vector bundles) and let M=A/~ be the set of equivalence classes. The
aim of the theory of moduli is to give M the structure of an algebraic
variety in a nice way. I will give a very elementary introduction to
this theory, considering the following questions: What data do we need to
formulate a moduli problem? What sort of solutions should we expect?
Under what conditions will a solution exist? I will look at a few
examples.
The talk will be based on Newstead's book "Introduction to moduli
problems and orbit spaces", which draws on ideas from Mumford's classic
book "Geometric invariant theory". My intention is that all of the
mathematical content of the talk will be at least as old as the speaker.
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