Genus formula $\;\;\;\;$

Question

Can someone give me a reference in which I can find the following result

Let $C$ be a curve, then $$g(C)=\frac{(n-1)(n-2)}{2}-s.$$

where $g=$ genus of $C,$ $n=$ degree of curve, $s=$ number of singular points.

Any help would be appreciated.

Answer 1

I know this is done in a series of exercises (this may be good news or not) at the end of Appendix A in Arbarello, Cornalba, Griffiths, and Harris, Geometry of Algebraic Curves, Volume I. They call it the "Gorenstein relation".

Answer 2

You can try books on algebraic geometry, and look for the genus formula, or Plücker formulas.