Are there any conditions on when an irreducible polynomial in several variables generate a maximal ideal?

Question

In the one variable case ($k[x]$ where $k$ is a field), we know that a polynomial is irreducible iff the ideal it generates is maximal. Now, reviewing the proof, it is clear that this proof doesn't carry over to the multivariable case, but are there any conditions on when a polynomial in $k[x_1,x_2,...,x_n]$ generates a maximal ideal? (We can assume k is a algebraically closed field).