ANAGRAMS

Student seminar

Goal

This series is intended to be an introduction to the subject. We will be working mostly with Mukai's excellent introduction [2] to the subject, and in some sense the first three weeks could be considered a reading seminar based on this book (although we will cover far from everything). So whenever things are unclear, expositions didn't cover a proof, or you wish to read about related things, consult this book.

Besides this book, there are also Dolgachev's lecture notes [4], which are a down-to-earth introduction to the subject, Tevelev's notes [5], which emphasise the moduli point of view and discuss weighted projective spaces explicitly.

The underlying goal of the seminar is to make Mumford's classic [GIT] a less daunting read, but no-one will be forced to read this wonderful, yet hard-to-crack classic.

After this we will discuss some applications of geometric invariant theory.

Schedule

February 28
Motivation for geometric invariant theory
Algebraic groups and actions
by Dennis Presotto and Theo Raedschelders, in G.017, at 10h00
March 7
Quotients of affine varieties, and projective quotients
By Kevin De Laet, in G.017, at 10h00
March 14
The Hilbert–Mumford criterion
Grassmannians
by Pieter Belmans and Julia Ramos González, in G.017, at 10h00
March 21
no lecture
March 28
Application: McKay correspondence (see [6,7])
by Kevin De Laet, in G.017, at 10h00
April 4
Application: Moduli of quiver representations
by Theo Raedschelders, in G.017, at 10h00

References

[1]
Schmitt, Alexander
Geometric invariant theory and decorated principal bundles
European Mathematical Society, 2008
[2]
Mukai, Shigeru
An introduction to invariants and moduli
Cambridge University Press, 2003(81)
[3]
Derksen, Harm and Kemper, Gregor
Computational invariant theory
Springer, 2002(130)
[4]
Dolgachev, Igor
Lectures on invariant theory (online)
Cambridge University Press, 2003(296)
[5]
Tevelev, Jenia
Moduli spaces and invariant theory (online)
[6]
Le Bruyn, Lieven
Quotient singularities and the conifold algebra (online)
[7]
Bocklandt, Raf
Kleinian singularities online)
[GIT]
Mumford, David
Geometric invariant theory
Springer-Verlag, 1965(34), pp. vi+145