Clemens' conjecture: part II

Details Clemens' conjecture: part II Clemens' conjecture: part II

2005-11-14

arxiv.org/abs/math/0511364v4

Mathematics

Algebraic Geometry

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Scientific paper

This is the part II of our series of two papers, "Clemens' conjecture: part I", "Clemens' conjecture: part II". Continuing from part I, in this paper we turn our attention to general quintic threefolds. In a universal quintic threefold X, we construct a family of quasi-regular deformation B_b such that the generic member in this family is non-deviated, but some special member is deviated. By the result from part I, this is impossible unless there is no one parameter family of smooth rational curves in a generic quintic threefold.

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