Some Results on the Degeneracy of Entire Curves and Integral Points in the Complements of Divisors

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dc.contributor.advisorRu, Min
dc.contributor.committeeMemberHeier, Gordon
dc.contributor.committeeMemberJi, Shanyu
dc.contributor.committeeMemberFeng, Qianmei
dc.creatorLiao, Hung Zen 1983-
dc.date.accessioned2019-11-13T03:23:52Z
dc.date.available2019-11-13T03:23:52Z
dc.date.createdDecember 2016
dc.date.issued2016-12
dc.date.submittedDecember 2016
dc.date.updated2019-11-13T03:23:52Z
dc.description.abstractIn this dissertation, we first discuss some of the important results in Nevanlinna Theory and Diophantine Approximation Theory. Next, a result by the author and Min Ru \cite{LR} is presented. In chapter 3, we extend the Second Main Theorem to the case of holomorphic curves into algebraic varieties intersecting numerically equivalent ample divisors. In chapter 4, we improve Ru's defect relation (see \cite{ru15}) and the height inequality (see \cite{ru}) in the case when $X$ is a normal projective surface and $D_j$, $1 \leq j \leq q$, are big and asymptotically free divisors without irreducible common components on $X$. Lastly, the author and Gordon Heier approach the hyperbolic problem by projections from $\mathbb{P}^{n+2}$ to $\mathbb{P}^{n}$.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10657/5410
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.subjectNavenlinna Theory
dc.subjectDiophantine approximation
dc.subjectHolomorphic curves
dc.titleSome Results on the Degeneracy of Entire Curves and Integral Points in the Complements of Divisors
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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