Hilbert schemes of points on surfaces

Details Hilbert schemes of points on surfaces Hilbert schemes of points on surfaces

2003-04-21

arxiv.org/abs/math/0304302v1

Proceedings of the ICM, Beijing 2002, vol. 2, 483--494

Mathematics

Algebraic Geometry

Scientific paper

The Hilbert scheme $S^{[n]}$ of points on an algebraic surface $S$ is a simple example of a moduli space and also a nice (crepant) resolution of singularities of the symmetric power $S^{(n)}$. For many phenomena expected for moduli spaces and nice resolutions of singular varieties it is a model case. Hilbert schemes of points have connections to several fields of mathematics, including moduli spaces of sheaves, Donaldson invariants, enumerative geometry of curves, infinite dimensional Lie algebras and vertex algebras and also to theoretical physics. This talk will try to give an overview over these connections.

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