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OverviewThe Hilbert scheme SX{[n] S of a surface SXS describes collections of SnS (not necessarily distinct) points on SXS. More precisely, it is the moduli space for S0S-dimensional subschemes of SXS of length SnS. Recently it was 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. The discussion in the book reflects this feature of Hilbert schemes. For example, a construction of the representation of the infinite dimensional Heisenberg algebra (i.e., Fock space) is presented. This representation has been studied extensively in the literature in connection with affine Lie algebras, conformal field theory, etc. However, the construction presented in this volume is completely unique and provides the unexplored link between geometry and representation theory. The book offers a nice survey of current developments in this rapidly growing subject. It is suitable as a text at the advanced graduate level. Full Product DetailsAuthor: Hiraku NakajimaPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: UK ed. Volume: No. 18 Dimensions: Width: 17.80cm , Height: 0.80cm , Length: 24.80cm Weight: 0.265kg ISBN: 9780821819562ISBN 10: 0821819569 Pages: 132 Publication Date: 30 September 1999 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Awaiting stock  The supplier is currently out of stock of this item. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out for you. Table of ContentsIntroduction 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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