• Lecturer: Javier Sendra Arranz, Ángel David Ríos Ortiz
• Date: March 14 at 15:00-17:10, March 16 at 11:00-14:30, March 21 at 11:00-12:00, March 23 at 11:00-14:30, March 24 at 10:00-12:10, March 28, 11:00-12:00
• Room: MPI MiS G3 10
• Keywords: Algebraic Geometry, Hilbert Schemes, Commutative Algebra

Abstract

The Hilbert scheme of a given projective variety is the scheme that parameterize all of its closed subschemes. As such it is ubiquitous in Algebraic Geometry, with connections with other areas of Mathematics and the Sciences. One of the celebrated results of Grothendieck was the construction of this scheme. The goal of this reading group will be to study the construction of the Hilbert scheme following a mostly explicit approach, explore its properties and give some examples and applications.

The schedule of the talks is the following

• March 14
  • Lecture 1 15:00-16:00, Speaker: Maximilian Wiesmann. Title: Introduction to Hilbert Schemes
  • Lecture 2 16:10-17:10, Speaker: Emeryck Marie. Title: Construction of the Hilbert Scheme
• March 16
  • Lecture 3 11:00-12:00, Speaker: Alexander Elzenaar. Title: Connectedness
  • Lecture 4 13:30-14:30, Speaker: Leo Kayser. Title: Smoothness
• March 21
  • 11:00-12:00 Exercises/Questions/Discussion
• March 23
  • Lecture 5 11:00-12:00, Speaker: Javier Sendra-Arranz. Title: Examples and pathologies
  • Lecture 6 13:30-14:30, Speaker: Barbara Betti and Stefano Mereta. Title: Multigraded Hilbert scheme
• March 24
  • Lecture 7 10:00-11:00, Speaker: Henry Robert Dakin. Title: Hilbert scheme of points on surfaces
  • Lecture 8 11:10-12:10, Speaker: Pierpaola Santarsiero and Casabella. Title: Applications of Hilbert Schemes
• March 28
  • 11:00-12:00 Exercises/Questions/Discussion