In the spring of 1996, I gave a series of lectures on the Hilbert schemes of points on surfaces at Department of Mathematical Sciences, University of Tokyo. The purpose of the lectures was to discuss various properties of the Hilbert schemes of points on surfaces. Although it was not noticed until recently, the Hilbert schemes have relationship with many other branch of mathematics, such as topology, hyperKahler geometry, symplectic geometry, singularities, and representation theory. This is reflected to this note: each chapter, which roughly corresponds to one lecture, discusses different topics. These lectures were intended for graduate students who have basic knowledge on algebraic geometry and ordinary topology. The only results which will be used but not proved in this note are Grothendieck's construction of the Hilbert scheme (Theorem 1.1) and results on intersection cohomology (ยง6.1). I recommend to the reader to accept these results when h

Authors: Nakajima H.  Pages: 121 Year: 1999 
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