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$\mu ^*$ -ZARISKI PAIRS OF SURFACE SINGULARITIES.
- Source :
-
Nagoya Mathematical Journal . Jun2024, Vol. 254, p488-497. 10p. - Publication Year :
- 2024
-
Abstract
- 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *HOMOGENEOUS polynomials
*COMPLEX variables
*ZETA functions
*TOPOLOGY
Subjects
Details
- Language :
- English
- ISSN :
- 00277630
- Volume :
- 254
- Database :
- Academic Search Index
- Journal :
- Nagoya Mathematical Journal
- Publication Type :
- Academic Journal
- Accession number :
- 177066285
- Full Text :
- https://doi.org/10.1017/nmj.2023.34