Abstract
We reprove (after a paper of Y.T. Siu appeared in 1987) a simple vanishing theorem for the Wronskian of Brody curves under a suitable assumption on the existence of global meromorphic connections. Next we give a slight improvement of a result due to Y.T, Siu and A.M. Nadel (Duke Math. J., 1989) on the algebraic degeneracy of entire holomorphic curves contained in certain hypersurfaces of ℙ ℂ n . Especially, their result is generalized to a larger class of hypersurfaces. Our method produces algebraic families of smooth hyperbolic surfaces in ℙ ℂ 3 for all degreesd≥14; this brings us somewhat nearer than previously known from the expected ranged≥5.
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