Abstract:
It's well-known that there is only one line
passing through two distinct points in C^3.
In the pre-colloquium
we will apply this fact to solve the following more complicated conditions,
with the aid of Chern classes:
- How many lines
passing through a fixed point and intersecting two fixed lines in C^3?
- How many lines intersecting four fixed lines in C^3?
- How many lines lying on a cubic surface in P^3?