Lectures on GEOMETRIC INVARIANT Theory & MODULI 1 | RADU LAZA

Lectures on GEOMETRIC INVARIANT Theory & MODULI
Radu Laza (Stony Brook University, USA)
School “Moduli of Curves” to be held from 22th February till 4th March, 2016 in CIMAT, Guanajuato, Mexico.

Abstract: Geometric Invariant Theory (GIT) is an important tool in the study of moduli spaces in algebraic geometry. In these lectures we will review the basic construction and properties of GIT quotients. We will also discuss some of the more recent developments including variation of GIT quotients (VGIT), the connections between GIT/VGIT and birational geometry, and the related notion of K-stability and the relationship to the existence of special metrics. We will close by reviewing some classical as well as more recent applications of GIT to moduli problems.

Standard References:
[GIT] D. Mumford et al., Geometric invariant theory, third ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2), vol. 34, Springer-Verlag, Berlin, 1994.
[Dol] I. V. Dolgachev, Lectures on invariant theory , London Mathematical Society Lecture Note Series, vol. 296, Cambridge University Press, Cambridge, 2003.
[Muk] S. Mukai, An introduction to invariants and moduli , Cambridge Studies in Advanced Mathematics, vol. 81, Cambridge University Press, Cambridge, 2003.

Surveys related to the lectures:
[Laz1] GIT and moduli with a twist, in "Handbook of Moduli" vol. 2, Adv. Lect. Math. 25 (2013), Int. Press, 259-297.
[Laz2] Perspectives on the construction and compactification of moduli spaces, Lectures for the school on "Compactifying Moduli Spaces" (Barcelona, May 2013), to appear in a volume of CRM Lecture Notes.