The ratio of Milnor number to Tjurina number for isolated hypersurface singularities is bounded above by a sharp constant depending on dimension, with μ/τ ≤ 3/2 for surfaces over the complex numbers.
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The Quotient of Milnor Number by Tjurina Number of Hypersurface Singularities in Arbitrary Characteristic
The ratio of Milnor number to Tjurina number for isolated hypersurface singularities is bounded above by a sharp constant depending on dimension, with μ/τ ≤ 3/2 for surfaces over the complex numbers.