Re:Any smooth cubic surface contains 27 lines
by infogulch on Wednesday February 17, 2016 @12:40AM
(#11115597)
So what can we say about 27 lines? Is it enough to just exclude the counterexample you gave? Say, is it true that:
All sets of 27 distinct lines describe a smooth cubic surface as long as no subset of 3 of them both intersect at the same point and are mutually orthogonal.
What additional restrictions would it take to know that the lines describe a distinct smooth cubic surface? (if that's possible at all)
All sets of 27 distinct lines describe a smooth cubic surface as long as no subset of 3 of them both intersect at the same point and are mutually orthogonal.
What additional restrictions would it take to know that the lines describe a distinct smooth cubic surface? (if that's possible at all)