Upper Bound on the Multiplicity of Rational and Du Bois Singularities

Key Points

• The aim is to determine a sharp upper bound for the multiplicity of Du Bois singularities in varieties.
• Proving a mathematical upper bound for multiplicity using combinatorial techniques.
• Analyzing the relationship between embedding dimension and dimension of varieties.
• Demonstrated that the multiplicity of Du Bois singularities is at most the binomial coefficient e choose d.
• Recovered the upper bound for rational singularities previously established.