Hilbert-Kunz multiplicity/Two-dimensional graded/Formula for maximal ideal in plane case/Fact

Let ${}R=K[x,y,z]/(H)$ be a normal homogeneous hypersurface domain of dimension two and degree ${}\delta$ over an algebraically closed field of positive characteristic.

Then there exists a rational number

${}\nu _{2}$, ${}{\frac {3}{2}}\leq \nu _{2}\leq 2$, such that the Hilbert-Kunz multiplicity of ${}R$ is

${}e_{HK}(R)=\delta {\left(\nu _{2}^{2}-3\nu _{2}+3\right)}\,.$

Write a proof