Holomorphic curves and integral points off divisors

We deal with the distributions of holomorphic curves and integral points off divisors. We will simultaneously prove an optimal dimension estimate from above of a subvariety W off a divisor D which contains a Zariski dense entire holomorphic curve, or a Zariski dense D-integral point set, provided that in the latter case everything is defined over a number field. Then, if the number of components of D is large, the estimate leads to the constancy of such a holomorphic curve or the finiteness of such an integral point set. At the beginning, we extend logarithmic Bloch-Ochiai's Theorem to the K?hler case. Received: 10 January 2000 / Published online: 18 January 2002