## If C⊆P2C \subseteq \mathbb{P}^2 is a plane curve, then genus(C)=12(d−1)(d−2)genus(C)=\frac{1}{2}(d-1)(d-2). Compare with example in the notes

In my Algebraic Geometry notes (see http://www.mathematik.uni-kl.de/~gathmann/class/alggeom-2002/main.pdf) there is the following exercise: If C⊆P2 is a plane curve of degree d, then its arithmetic genus g(C) is equal to 12(d−1)(d−2). Compare this to example 0.1.3 (of the notes of course). In fact, the first part of the exercise is easy to solve using the Hilbert … Read more