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Hilbert Schemes of Points and Infinite Dimensional Lie Algebras (Mathematical Surveys and Monographs)

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£97.91 £88.25 £90.36 £92.47 £94.57 £96.68 £98.79 26 April 2026 14 May 2026 02 June 2026 20 June 2026 09 July 2026

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Description

About the Author Zhenbo Qin, University of Missouri, Columbia, MO. Product Description Hilbert schemes, which parametrize subschemes in algebraic varieties, have been extensively studied in algebraic geometry for the last 50 years. The most interesting class of Hilbert schemes are schemes $X^{[n]}$ of collections of $n$ points (zero-dimensional subschemes) in a smooth algebraic surface $X$. Schemes $X^{[n]}$ turn out to be closely related to many areas of mathematics, such as algebraic combinatorics, integrable systems, representation theory, and mathematical physics, among others.This book surveys recent developments of the theory of Hilbert schemes of points on complex surfaces and its interplay with infinite dimensional Lie algebras. It starts with the basics of Hilbert schemes of points and presents in detail an example of Hilbert schemes of points on the projective plane. Then the author turns to the study of cohomology of $X^{[n]}$, including the construction of the action of infinite dimensional Lie algebras on this cohomology, the ring structure of cohomology, equivariant cohomology of $X^{[n]}$ and the Gromov-Witten correspondence. The last part of the book presents results about quantum cohomology of $X^{[n]}$ and related questions.The book is of interest to graduate students and researchers in algebraic geometry, representation theory, combinatorics, topology, number theory, and theoretical physics.

Product Specifications

Format
hardcover
Domain
Amazon UK
Release Date
30 March 2018
Listed Since
15 December 2017

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