Hi am a student of Maths at university; I am studying the theorem of Riemann-Roch for curves. I am interested in understanding what happens in the case of surfaces. I do not want to look for the whole proof, because it is far beyond my actual math knowledge, but I would like to see an example of what happens. Could you please give me a reference where I can find a worked example of what happens in the case of surfaces (obviously I do not expect you to write it here to me)?
Thank you in advance!
I have written a small project about this, mainly based on Hartshorne's 'Algebraic Geometry'. I use the version $ l(D)-s(D)+l(K-D) = \frac{1}{2} D. (D-K) + 1 + p_a(X)$ of the Riemann-Roch theorem for surfaces. Normally this should be the link