Hilbert-Kunz Multiplizität/Zweidimensional graduiert/Formel für maximales Ideal im ebenen Fall/en/Fakt

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

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

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