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dc.contributor.advisorQin, Zhenboeng
dc.contributor.authorMurphy, Ryan, 1983-eng
dc.date.issued2010eng
dc.date.submitted2010 Falleng
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on March 7, 2011).eng
dc.descriptionThe 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.descriptionDissertation advisor: Dr. Zhenbo Qin.eng
dc.descriptionVita.eng
dc.descriptionIncludes bibliographical references.eng
dc.descriptionPh. D. University of Missouri--Columbia 2010.eng
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Mathematics.eng
dc.description.abstractThis 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.extent75 pageseng
dc.identifier.oclc707637646eng
dc.identifier.urihttps://hdl.handle.net/10355/10280
dc.identifier.urihttps://doi.org/10.32469/10355/10280eng
dc.languageEnglisheng
dc.publisherUniversity of Missouri--Columbiaeng
dc.relation.ispartofcommunityUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.rights.licenseThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License.
dc.subject.lcshHilbert schemeseng
dc.subject.lcshProjective planeseng
dc.subject.lcshCohomology operationseng
dc.titleA transition matrix for two bases of the integral cohomology of the Hilbert scheme of points in the projective planeeng
dc.typeThesiseng
thesis.degree.disciplineMathematics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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