Hi all,

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 $\displaystyle D$ is any divisor on a non-singular projective algebraic curve in $\displaystyle P_2$, and $\displaystyle \kappa $ a canonical divisor, then $\displaystyle l(D)-l(\kappa - D)=deg(D)+1-g$.

My lecture notes immediately after the statement of the theorem make the following point: If $\displaystyle deg(D) > 2g-2,$ then $\displaystyle deg(\kappa-D) <0,$ so.... etc.

I don't really see at all how this follows, any tips?