Lines on contact Manifolds IIb
摘要
Let X be a complex-projective contact manifold whose second Betti-number is one. It has long been conjectured that X should then be rational-homogeneous, or equivalently, that there exists an embedding of X into a projective space whose image contains lines. Using methods introduced in math.AG/0206193, we show that X is covered by a compact family of rational curves, called "contact lines" that behave very much like the lines on the rational homogeneous examples: if x in X is a general point, then all contact lines through x are smooth, no two of them share a common tangent direction at x, and the union of all contact lines through x forms a cone over an irreducible, smooth base. As a corollary, we obtain that the tangent bundle of X is stable.
引用
@article{arxiv.math/0306260,
title = {Lines on contact Manifolds IIb},
author = {Stefan Kebekus},
journal= {arXiv preprint arXiv:math/0306260},
year = {2007}
}
备注
Fixed a number of minor issues found by the referee. To appear in Compositio Math. A PDF-file with additional graphics is available on the internet at http://www.mi.uni-koeln.de/~kebekus/publications-e.html