We 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 filll 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.
On quadrisecant lines of threefolds in P^5
MEZZETTI, EMILIA
2001-01-01
Abstract
We 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 filll 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.File in questo prodotto:
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