Symmetrische Hilbert Kunz Theorie/Funktion über Kokern/en/Definition

For a homogeneous ${}R_{+}$-primary ideal ${}I$ in a two-dimensional standard-graded normal domain ${}R$ we define

${}\varphi _{I}^{S}(q)=\sum _{m=0}^{\infty }\operatorname {dim} _{K}\,(\operatorname {coker} \,\psi _{q,m})\,$

and call this the symmetric Hilbert-Kunz function.