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Lectures on Hilbert Schemes of Points on Surfaces
     

Lectures on Hilbert Schemes of Points on Surfaces

by Hiraku Nakajima
 

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 The Hilbert scheme of a surface $X$ describes collections of $n$ (not necessarily distinct) points on $X$. More

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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 The Hilbert scheme 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. One example of the modern, broader interest in the subject is a construction of the representation of the infinite-dimensional Heisenberg algebra, i.e., Fock space. 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 an unexplored link between geometry and representation theory. The book offers an attractive survey of current developments in this rapidly growing subject. It is suitable as a text at the advanced graduate level.

Editorial Reviews

Booknews
The author discusses the Hilbert scheme of points X[n] on a complex surface X from various points of view. It inherits structures of X, e.g. it is a nonsingular complex manifold, it has a holomorphic symplectic form if X has one, and so on. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Product Details

ISBN-13:
9780821819562
Publisher:
American Mathematical Society
Publication date:
01/01/1999
Series:
University Lecture Series , #18
Pages:
132
Product dimensions:
7.98(w) x 8.06(h) x 0.24(d)

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