Lectures on Hilbert Schemes of Points on Surfaces (University Lecture Series) - Softcover

Hiraku Nakajima

Softcover

ISBN 10: 0821819569 ISBN 13: 9780821819562

Publisher: American Mathematical Society, 1999

Synopsis

The Hilbert scheme $X^{[n]}$ of a surface $X$ describes collections of $n$ (not necessarily distinct) points on $X$. More precisely, it is the moduli space for $0$-dimensional subschemes of $X$ of length $n$. 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.

About this title

From the Publisher

"This beautifully written book deals with one shining example: the Hilbert schemes of points on algebraic surfaces ... The topics are carefully and tastefully chosen ... The young person will profit from reading this book."
-- Mathematical Reviews

Edition details

• Publisher: American Mathematical Society
• Publication date: 1999
• Language: English
• ISBN 10: 0821819569
• ISBN 13: 9780821819562
• Binding: Paperback
• Number of pages: 132