On quadrisecant lines of threefolds in P^5
AbstractWe study smooth threefolds of P^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 P^5 , 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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