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GIT Reading Group

  • Raluca Vlad (Harvard University)
  • Yassine El Maazouz (University of California, Berkeley)
G3 10 (Lecture hall)

Abstract

Geometric Invariant Theory studies how to construct group quotients in Algebraic Geometry. The motivation behind the construction of such quotients lies in the frame of moduli problems. It provides indeed a method for constructing moduli space. In this reading group we will study the theoretical tools necessary for constructing affine and projective GIT quotients for reductive groups with the final goal of constructing the moduli space of projective hypersurfaces. In particular, we will give an introduction to moduli problems, algebraic groups, algebraic actions, geometric quotients, GIT quotients, etc. We will follow the lecture notes by Victoria Hoskins, from which we will cover section 1-7.

There will be a short introduction of 15 mins, followed by a talk from Raluca Vlad 14:00-15:00 and Yassine El Maazouz 15:00-16:00.

References:

Main reference: Hoskins, V. (2016). Moduli problems and geometric invariant theory. Lecture Notes, available at userpage.fu-berlin.de/hoskins/M15_Lecture_notes.pdf

Others:

  • Mukai, S., & Shigeru, M. (2003). An introduction to invariants and moduli (Vol. 81). Cambridge University Press.
  • Mumford, D. (1965). Geometric Invariant Theory.
  • Dolgachev, I. (2003). Lectures on invariant theory (No. 296). Cambridge University Press.

Mirke Olschewski

MPI for Mathematics in the Sciences Contact via Mail