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 dc.contributor.advisor Qin, Zhenbo eng dc.contributor.author Murphy, Ryan, 1983- eng dc.date.issued 2010 eng dc.date.submitted 2010 Fall eng dc.description Title from PDF of title page (University of Missouri--Columbia, viewed on March 7, 2011). eng dc.description The entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file. eng dc.description Dissertation advisor: Dr. Zhenbo Qin. eng dc.description Vita. eng dc.description Includes bibliographical references. eng dc.description Ph. D. University of Missouri--Columbia 2010. eng dc.description Dissertations, Academic -- University of Missouri--Columbia -- Mathematics. eng dc.description.abstract This work is devoted to comparing two integral bases for the integral cohomology of the Hilbert scheme of points in the projective plane. Let X be a smooth complex projective surface. One of the more interesting moduli spaces parameterizing objects associated with X is the Hilbert scheme of points, denoted X[superscript [n]], which parameterizes all 0-dimensional closed subschemes of length n in X. W. Wang, Z. Qin and W.P. Li used Heisenberg algebra operators to construct an integral basis of the integral cohomology of X[superscript [n]] whenever X is a smooth projective surface with vanishing odd Betti numbers. On the other hand, a work by G. Ellingsrud and S.A. Strømme gives a cellular decomposition of the Hilbert scheme of points on the projective plane. From this work, we have a second integral basis for the integral cohomology of X[superscript [n]] when X = P². We compare the elements of these two bases and ultimately give the upper triangular transition matrix from one basis to the other. eng dc.format.extent 75 pages eng dc.identifier.oclc 707637646 eng dc.identifier.uri https://hdl.handle.net/10355/10280 dc.identifier.uri https://doi.org/10.32469/10355/10280 eng dc.language English eng dc.publisher University of Missouri--Columbia eng dc.relation.ispartofcommunity University of Missouri--Columbia. Graduate School. Theses and Dissertations eng dc.rights.license This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. dc.subject.lcsh Hilbert schemes eng dc.subject.lcsh Projective planes eng dc.subject.lcsh Cohomology operations eng dc.title A transition matrix for two bases of the integral cohomology of the Hilbert scheme of points in the projective plane eng dc.type Thesis eng thesis.degree.discipline Mathematics (MU) eng thesis.degree.grantor University of Missouri--Columbia eng thesis.degree.level Doctoral eng thesis.degree.name Ph. D. eng
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