How to find a regular parameter system of the local ring $ \mathbb{C} [X_0, \dots, X_n]_{(P \ )} $?

89 Views Asked by At

How to find a regular parameter system of the local ring : $ \mathbb{C} [X_0, \dots, X_n]_{(P \ )} $ with : $ (P \ ) $ a prime ideal of : $ \mathbb{C} [X_0, \dots, X_n] $ ( i.e : $ P \in \mathbb{C} [X_0, \dots, X_n] $ is an irreducible homogeneous polynomial ) ?

$ \mathbb{C} [X_0, \dots, X_n] $ is the ring of homogeneous polynomials in : $ X_0, \dots, X_n $.

Thanks in advance for your help.