On quadrisecant lines of threefolds in P^5

Details On quadrisecant lines of threefolds in P^5 On quadrisecant lines of threefolds in P^5

2001-12-07

arxiv.org/abs/math/0112075v1

Mathematics

Algebraic Geometry

Plain Tex, 12 pages

Scientific paper

We study smooth threefolds of the projective space of dimension 5 whose quadrisecant lines don't fill up the space. We give a complete classification of those threefolds X whose only quadrisecant lines are the lines contained in X. Then we prove that, if X admits "true" quadrisecant lines, but they don't fill up the space, then either X is contained in a cubic hypersurface, or it contains a family of dimension at least two of plane curves of degree at least four.

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