We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
$\mu ^*$-ZARISKI PAIRS OF SURFACE SINGULARITIES
Let 
$f_0$ and 
$f_1$ be two homogeneous polynomials of degree d in three complex variables 
$z_1,z_2,z_3$. We show that the Lê–Yomdin surface singularities defined by 
$g_0:=f_0+z_i^{d+m}$ and 
$g_1:=f_1+z_i^{d+m}$ have the same abstract topology, the same monodromy zeta-function, the same 
$\mu ^*$-invariant, but lie in distinct path-connected components of the 
$\mu ^*$-constant stratum if their projective tangent cones (defined by 
$f_0$ and 
$f_1$, respectively) make a Zariski pair of curves in 
$\mathbb {P}^2$, the singularities of which are Newton non-degenerate. In this case, we say that 
$V(g_0):=g_0^{-1}(0)$ and 
$V(g_1):=g_1^{-1}(0)$ make a 
$\mu ^*$-Zariski pair of surface singularities. Being such a pair is a necessary condition for the germs 
$V(g_0)$ and 
$V(g_1)$ to have distinct embedded topologies.
