Whenever, people talk about singular plane curves they talk about their Newton polytope which is obviously coordinate dependent. I understand that with some conditions over the singular curve, some invariantes can be calculated from the Newton polytope e.g the multiplier ideal of the monomial ideal $(x^p,y^q)$ is the same than the one of the polynomial $x^p+y^q$. I am also aware that under some non degeneracy conditions you can use the Newton polytope for finding Hodge numbers, Milnor number, etc. However, I am not able to find a reference for equisingularity i.e topological equivalent. Two different curves with the same Newton polytope are equisingular? If not, can I impose restriction over the curves for having this property?



Does the Newton polytope characterize the equisingular i.e topological type?
The answer is **yes**.


More precisely, if two *nondegenerate* Newton singularities $f(x,y)=0$ and $g(x,y)=0$ have the same Newton polygon, then they are topologically equivalent. 


For a reference, look at Takamura's book "Splitting deformations of degenerations of complex curves III", [pag. 138](http://books.google.com/books?id=YWUV0XCwwT4C&pg=PA138&lpg=PA138&dq=singularities+with+the+same+newton+polygon&source=bl&ots=c_r5w2f6w6&sig=uXFd50WrelB2-ixZlBaDfS1Pcjc&hl=en&ei=mQtqTrLoKs-d-QapuODSBA&sa=X&oi=book_result&ct=result&resnum=2&ved=0CB0Q6AEwAQ), in particular at the note after Theorem 7.4.1. 


