English

Clemens' conjecture: part I

Algebraic Geometry 2011-07-26 v4

Abstract

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.

Keywords

Cite

@article{arxiv.math/0511312,
  title  = {Clemens' conjecture: part I},
  author = {Bin Wang},
  journal= {arXiv preprint arXiv:math/0511312},
  year   = {2011}
}

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