I have some questions regarding the divisors and the Riemann-Roch theorem.
1. What exactly is a hyperplane divisor? I cannot find the definition of it in any of my books or notes, and not even google was of assistance this time. The term first came up on a past paper, but I have never seen it before.
2. Riemann-Roch tells us that if is any divisor on a non-singular projective algebraic curve in , and a canonical divisor, then .
My lecture notes immediately after the statement of the theorem make the following point: If then so.... etc.
I don't really see at all how this follows, any tips?