- Modular forms on the moduli space of polarised K3 surfaces
- Award date
- 19 June 2015
- Number of pages
- Document type
- PhD thesis
- Faculty of Science (FNWI)
- Korteweg-de Vries Institute for Mathematics (KdVI)
This thesis concerns a subject from algebraic geometry, a branch of mathematics. Geometry is the study of spatial structures; algebraic geometry looks at spatial objects that can be described using polynomial formulas and uses abstract algebraic methods to study properties of those objects. The possibility to use the power and precision of algebraic methods in combination with geometric intuition makes this a beautiful subject. K3 surfaces are a class of 2-dimensional geometric objects. There are infinitely many distinct K3 surfaces; it is not possible to enumerate them all. However, it is possible to create a "catalogue", in which every possible K3 surface occurs exactly once.
This catalogue itself can be seen to be a geometric object; it is called the moduli space of K3 surfaces. A point of this moduli space corresponds to a particular K3 surface; a small displacement within the moduli space gives a small deformation of the surface. In this thesis we study the structure of the moduli space of K3 surfaces. It turns out that so-called modular forms are relevant to this. These are functions that behave in a very special way under the action of a discrete group of transformations. These modular forms contain a surprising amount of number-theoretic information.
- Research conducted at: Universiteit van Amsterdam
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