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.
Speakers will be Angel David Rios Ortiz 15:00-16:00 and Clemens Nollau 16:00-17:00.
References:
Main reference: Hoskins, V. (2016). Moduli problems and geometric invariant theory. Lecture Notes, available at https://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.
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 talk by Javier Sendra-Arranz 16:00-17:00 and Exercises 17:00-18:00.
References:
Main reference: Hoskins, V. (2016). Moduli problems and geometric invariant theory. Lecture Notes, available at https://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.
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.
Speakers will be Claudia Fevola 14:30-15:30 and Pierpaola Santarsiero 15:30-16:30.
References:
Main reference: Hoskins, V. (2016). Moduli problems and geometric invariant theory. Lecture Notes, available at https://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.
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 https://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.
