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dc.contributor.authorStaal, Andrew P.en
dc.date2016-09-11 13:52:03.771
dc.date.accessioned2016-09-13T19:17:11Z
dc.date.available2016-09-13T19:17:11Z
dc.date.issued2016-09-13
dc.identifier.urihttp://hdl.handle.net/1974/14882
dc.descriptionThesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2016-09-11 13:52:03.771en
dc.description.abstractWe prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.en
dc.language.isoengen
dc.relation.ispartofseriesCanadian thesesen
dc.rightsQueen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canadaen
dc.rightsProQuest PhD and Master's Theses International Dissemination Agreementen
dc.rightsIntellectual Property Guidelines at Queen's Universityen
dc.rightsCopying and Preserving Your Thesisen
dc.rightsThis publication is made available by the authority of the copyright owner solely for the purpose of private study and research and may not be copied or reproduced except as permitted by the copyright laws without written authority from the copyright owner.en
dc.subjectlexicographic idealen
dc.subjectK-polynomialen
dc.subjectHilbert schemeen
dc.subjectHilbert polynomialen
dc.subjectstrongly stable idealen
dc.titleIrreducibility of Random Hilbert Schemesen
dc.typethesisen
dc.description.degreePhDen
dc.contributor.supervisorSmith, Gregory G.en
dc.contributor.departmentMathematics and Statisticsen
dc.degree.grantorQueen's University at Kingstonen


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