An Improved Defect Relation for Holomorphic Curves in Projective Varieties

In this dissertation we improve Min Ru's defect relation (as well as the Second Main Theorem) for holomorphic curves $f:C\to X$ intersecting $D:=D1+\cdots +Dq$, where $D$ is a divisor of equi-degree, and $D1,\dots ,Dq$ are big, nef, and have no components in common. Our results will decrease the number of divisors $Di$ that $f$ is needed to omit in order to conclude that $f$ is degenerate. The corresponding arithmetic results are also obtained.