Blow Ups and Deformations: an Introduction to the Theory of Singularities

Course manual 2021/2022

Course content

A geometrical object is smooth if the tangent space is well-defined and has everywhere the same dimension.
A geometrical object is singular if this is not the case and points where the tangent space is too large are called
singularities. In general singular space are much harder to study than smooth spaces and therefore it is important
to turn a singular space into a smooth one. In this course we will study 2 different ways to smoothen singularities:
deforming and blowing up. We will study these two ways in detail and apply them to an important
class of singularities: the simple singularities.

Objectives

• calculate the Jacobi algebra of a singularity.
• Deform a simple singularity
• Use representation theory to resolve a singularity
• give the definition of a singularity and determine all singular points of a hypersurface.
• Blow up a simple singularity
• describe the classification of simple singularities

Teaching methods

• Lecture

The course will consist of theory lectures mixed with some exercises during class. 

Learning activities

Attendance

This programme does not have requirements concerning attendance (TER-B).

Assessment

The student needs to get 6/10 for the final mark

Assignments

The students will investigate some singularities using Macauley2

Fraud and plagiarism

The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl

Course structure

Timetable

The schedule for this course is published on DataNose.

Contact information

Coordinator

• Raf Bocklandt