Genus-degree formula
= Genus-degree formula
{wiki}
The arithmetic genus of a degree-$d$ <projective plane curve> is
$$
p_a=\frac{(d-1)(d-2)}2.
$$
Equivalently, its structure sheaf has Euler characteristic $\chi(\mathcal O_X)=1-p_a$.
= Genus-degree formula
{wiki}
The arithmetic genus of a degree-$d$ <projective plane curve> is
$$
p_a=\frac{(d-1)(d-2)}2.
$$
Equivalently, its structure sheaf has Euler characteristic $\chi(\mathcal O_X)=1-p_a$.