Lectures on Hilbert Schemes of Points on Surfaces is popular PDF and ePub book, written by Hiraku Nakajima in 2024-10-01, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lectures on Hilbert Schemes of Points on Surfaces can be Read Online from any device for your convenience.
Lectures on Hilbert Schemes of Points on Surfaces Book PDF Summary
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.
Detail Book of Lectures on Hilbert Schemes of Points on Surfaces PDF
- Author : Hiraku Nakajima
- Release : 01 October 2024
- Publisher : American Mathematical Soc.
- ISBN : 0821882767
- Genre : Mathematics
- Total Page : 148 pages
- Language : English
- PDF File Size : 14,7 Mb
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