The Zariski multiplicity conjecture asks whether the embedded topological germ of a reduced complex hypersurface determines its multiplicity. For a nonzero convergent
power series 
vanishing at the origin, the multiplicity is 
, the least total degree
of a nonzero monomial. Reduced means that no irreducible factor is repeated. The
topological equivalence is a homeomorphism germ of ambient
pairs, fixing the origin and carrying one zero set onto
the other.
Zariski Multiplicity Conjecture
See also
Germ, Homeomorphism, Hypersurface, Multiplicity, Singularity, Weighted Homogeneous PolynomialExplore with Wolfram|Alpha
References
Seade, J. "On Milnor's Fibration Theorem and Its Offspring After 50 Years." Bull. Amer. Math. Soc. 56, 281-348, 2019. https://doi.org/10.1090/bull/1654.Cite this as:
Weisstein, Eric W. "Zariski Multiplicity Conjecture." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ZariskiMultiplicityConjecture.html