
RiemannRoch theorem
Hi all,
I have some questions regarding the divisors and the RiemannRoch 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. RiemannRoch tells us that if $\displaystyle D$ is any divisor on a nonsingular projective algebraic curve in $\displaystyle P_2$, and $\displaystyle \kappa $ a canonical divisor, then $\displaystyle l(D)l(\kappa  D)=deg(D)+1g$.
My lecture notes immediately after the statement of the theorem make the following point: If $\displaystyle deg(D) > 2g2,$ then $\displaystyle deg(\kappaD) <0,$ so.... etc.
I don't really see at all how this follows, any tips?
Thanks,
Aliquantus