A General Defect Relation and Height Inequality for Divisors in Subgeneral Position

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dc.contributor.advisorRu, Min
dc.contributor.committeeMemberHeier, Gordon
dc.contributor.committeeMemberJi, Shanyu
dc.contributor.committeeMemberFeng, Qianmei
dc.creatorHussein, Saud 1975-
dc.date.accessioned2018-11-30T21:16:08Z
dc.date.available2018-11-30T21:16:08Z
dc.date.createdAugust 2016
dc.date.issued2016-08
dc.date.submittedAugust 2016
dc.date.updated2018-11-30T21:16:08Z
dc.description.abstractIn this dissertation, we describe a paper that improves on the conditions that imply holomorphic curves and integral points are degenerate or not Zariski-dense. Specifically, we show that for a holomorphic curve into a projective variety of dimension n intersecting q divisors in subgeneral position whose sum is equidegreelizable, if q is greater than or equal to n 2 , then the curve is degenerate. This is an improvement from 2n 2 under the same conditions in paper. To achieve this result, we borrow methods from that combine divisors in pairs and uses a joint filtration result from linear algebra. Lastly, a pointwise filtration approach, first considered by Corvaja, Levin, and Zannier, is used to give further improvements such that if q is greater than or equal to n 2 − n, then the curve is degenerate. This pointwise filtration may be constructed by using linear algebra on the power series locally representing the sections.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10657/3550
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectNevanlinna theory
dc.subjectDiophantine approximation
dc.subjectDefect relation
dc.subjectEquidegree
dc.subjectSubgeneral position
dc.titleA General Defect Relation and Height Inequality for Divisors in Subgeneral Position
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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