Siegel’s theorem on integer points: Let $P \in {\mathbb{Q}}[x,y]$ be an irreducible polynomial of two variables, such that the affine plane curve $C = \{ (x,y): P(x,y)=0\}$ either has genus at least one, or has at least three points on the line at infinity, or both. Then $C$ has only finitely many integer points $(x,y) \in \mathbb{Z}\times\mathbb{Z}.$
Question: Is there any generalization for irreducible polynomials on more variables?