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

In 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.

Name thesis:degree_name

Doctor of Philosophy

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Houston

Year dc:date.issued

2016

Author dc:creator

• Liao, Hung Zen 1983-

Advisor dc:contributor.advisor

• Ru, Min

Committee members dc:contributor.committeemember

• Heier, Gordon
• Ji, Shanyu
• Feng, Qianmei

• Navenlinna Theory
• Diophantine approximation
• Holomorphic curves

Statement dc:rights

• The 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).

Language dc:language.iso

eng

Handle dc:identifier.uri

https://hdl.handle.net/10657/5410

OAI identifier oai:identifier

oai:uh-ir.tdl.org:10657/5410