Es sei ${\displaystyle {}K}$ ein Körper und ${\displaystyle {}K[X_{1},\ldots ,X_{n}]}$ der Polynomring über ${\displaystyle {}K}$ in ${\displaystyle {}n}$ Variablen und ${\displaystyle {}K[X_{1},\ldots ,X_{n},Z]}$ der Polynomring in ${\displaystyle {}n+1}$ Variablen. Zu ${\displaystyle {}F\in K[X_{1},\ldots ,X_{n}]}$ sei ${\displaystyle {}{\hat {F}}\in K[X_{1},\ldots ,X_{n},Z]}$ die Homogenisierung (bezüglich ${\displaystyle {}Z}$) und zu ${\displaystyle {}G\in K[X_{1},\ldots ,X_{n},Z]}$ sei ${\displaystyle {}{\tilde {G}}}$ die (durch ${\displaystyle {}Z\mapsto 1}$ gegebene) Dehomogenisierung

${\displaystyle {}G}$

${\displaystyle {}{\tilde {\hat {F}}}=F}$

${\displaystyle {}{\hat {\tilde {G}}}=G}$