Clemens' conjecture: part I

Details Clemens' conjecture: part I Clemens' conjecture: part I

2005-11-14

arxiv.org/abs/math/0511312v4

Mathematics

Algebraic Geometry

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Scientific paper

This is a series of two papers in which we solve the Clemens conjecture: there are only finitely many smooth rational curves of each degree in a generic quintic threefold. In this first paper, we deal with a family of smooth Calabi-Yau threefolds f_\epsilon for a small complex number \epsilon. We give an geometric obstruction, deviated quasi-regular deformations B_b of c_\epsilon, to a deformation of the rational curve c_\epsilon in a Calabi-Yau threefold f_\epsilon.

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