# Hilbert Schemes

**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

- Lecture 1 15:00-16:00, Speaker:
**March 16**- Lecture 3 11:00-12:00, Speaker:
*Alexander Elzenaar*. Title: Connectedness - Lecture 4 13:30-14:30, Speaker:
*Leo Kayser*. Title: Smoothness

- Lecture 3 11:00-12:00, Speaker:
**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

- Lecture 5 11:00-12:00, Speaker:
**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

- Lecture 7 10:00-11:00, Speaker:
**March 28**- 11:00-12:00 Exercises/Questions/Discussion

## Regular lectures: Winter semester 2022/2023

**Hilbert Schemes**- Javier Sendra Arranz, Ángel David Ríos Ortiz
- 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, MPI MiS G3 10

**IMPRS Ringvorlesung**- Tobias Ried, Florentin Münch, Dejan Gajic, Stefan Czimek
- Mondays 10.30-12.00 (please note special dates and rooms at the lectures), MPI MiS E1 05 (Leibniz)
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**Mathematical foundations of data anlaysis**- Samantha Fairchild
- Tuesdays 11:15-12:45 and Wednesdays 15:15-16:45, SG 2-14
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**Bielefeld-Leipzig online seminar: Mathematics of Machine Learning**- Benjamin Gess
- Wednesdays 16:15-17:45, Videobroadcast
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**Topics in the Spatially Homogeneous Boltzmann Equation**- Daniel Heydecker
- Wednesdays, 14:00-15:30, MPI MiS A3 01
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**Principles of Network Analysis**- Jürgen Jost, Raffaella Mulas
- Friday, 2-3.30pm
**(Attention: On 14.10. in room A3 01)**, MPI MiS E1 05 (Leibniz) - To keep informed about changes to this lecture subscribe to lecture mailinglist

**Nonlinear potential theory for degenerate elliptic PDE**- Lukas Koch
- Thursdays, 09.00-10.30, MPI MiS A3 01
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**Recent developments in discrete Ricci curvature**- Florentin Münch
- Thursday, 15.00-16.30, MPI MiS A3 01
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**Mukai Grassmannians**- Angel Rios
- 12 lectures on Tuesdays 10:00 - 11:30 and Thursdays, 10:30 - 12:00 starting September 20, MPI MiS G3 10
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**Random Topology**- Erika Roldan, Sayan Mukherjee
- Tuesdays, 13:30-15:00, MPI MiS A3 01
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**Algebraische Geometrie**- Rainer Sinn
- Wednesday 11-13 and Thursday 15-17, P701 (voraussichtlich)
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**Metric Algebraic Geometry**- Bernd Sturmfels
- Tuesdays 17:10-18:30, Videobroadcast

**Lecture course on optimal transport**- Max von Renesse
- Friday 09.15 -- 10.45 CET, starting Oct 28., Videobroadcast