Irreducibility of Random Hilbert Schemes
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Authors
Staal, Andrew P.
Date
2016-09-13
Type
thesis
Language
eng
Keyword
lexicographic ideal , K-polynomial , Hilbert scheme , Hilbert polynomial , strongly stable ideal
Alternative Title
Abstract
We 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.
Description
Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2016-09-11 13:52:03.771
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Queen's University's Thesis/Dissertation Non-Exclusive License for Deposit to QSpace and Library and Archives Canada
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Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This 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.
ProQuest PhD and Master's Theses International Dissemination Agreement
Intellectual Property Guidelines at Queen's University
Copying and Preserving Your Thesis
This 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.