How can I parametrize a line in $\mathbb {CP}^1\times\mathbb{CP}^1$?
I've found something call the Segre map, but I do not know how to use it. The only thing I want to know is how they look like; they could be a zero locus of a certain polynomial or something like that.
And, the other question is, How many lines pass through two given points in $\mathbb {CP}^1\times\mathbb{CP}^1$?
By a line in {CP}^1\times\mathbb{CP}^1$ I mean a copy of {CP}^1 :)
Thank you.