Lectures on Hilbert Schemes of Points on Surfaces
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A01=American Mathematical Society
Author_American Mathematical Society
Category=PBMW
Category=PBP
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Product details
- ISBN 9780821819562
- Weight: 265g
- Publication Date: 30 Sep 1999
- Publisher: American Mathematical Society
- Publication City/Country: US
- Product Form: Paperback
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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.
