Description

Book Synopsis
It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

Table of Contents
Introduction Hilbert scheme of points Framed moduli space of torsion free sheaves on $\mathbb{P}^2$ Hyper-Kahler metric on $(\mathbb{C}^2)^{[n]}$ Resolution of simple singularities Poincare polynomials of the Hilbert schemes (1) Poincare polynomials of Hilbert schemes (2) Hilbert scheme on the cotangent bundle of a Riemann surface Homology group of the Hilbert schemes and the Heisenberg algebra Symmetric products of an embedded curve, symmetric functions and vertex operators Bibliography Index.

Lectures on Hilbert Schemes of Points on Surfaces

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      Book details

      Publisher American Mathematical Society
      Published 9/30/1999 12:00:00 AM
      ISBN-13 9780821819562
      978-0821819562
      ISBN-10 0821819569

      Description

      Book Synopsis
      It has been realized that Hilbert schemes originally studied in algebraic geometry are closely related to several branches of mathematics, such as singularities, symplectic geometry, representation theory - even theoretical physics. This book reflects this feature of Hilbert schemes.

      Table of Contents
      Introduction Hilbert scheme of points Framed moduli space of torsion free sheaves on $\mathbb{P}^2$ Hyper-Kahler metric on $(\mathbb{C}^2)^{[n]}$ Resolution of simple singularities Poincare polynomials of the Hilbert schemes (1) Poincare polynomials of Hilbert schemes (2) Hilbert scheme on the cotangent bundle of a Riemann surface Homology group of the Hilbert schemes and the Heisenberg algebra Symmetric products of an embedded curve, symmetric functions and vertex operators Bibliography Index.

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