some classical "line geometry" Schubert, over 100 years ago, considered questions like this: given several lines Li in space, how many lines M meet all of them? For instance if there is only one line L to begin with, we can pass lots of lines M through every point of L. Indeed if we choose a plane P off somewhere, then each point of L and each point of P determine a line meeting L, so there are at least a three dimensional infinity of them, one dimensions for the choice of a point of L, and 2 more for the choice of a point of P. If we choose two lines L1 and L2. then for each point of L1 and each point of L2 there is a unique line through both points, hence a doubly infinite family of lines meeting both. If we choose three lines L1, L2, L3, then if we fix a point x on L1, and conside all lines through x and also thropugh some point of L2, we get a one dimensional family of lines sweeping out a plane, which polane should meet L3 somewhere, so we get one line throughx meeting both L2 and L3. Since we can do this for each point x on L1, we get a one dimensional infinity of lines meeting all 3 lines. Now what if we have 4 lines L1, L2, L3, L4? There will presumably be only a finite number of lines meeting all 4? But how many? This is sort of the first problem in "enumerative geometry".