Segre Numbers and Hypersurface Singularities

Abstract

We define the Segre numbers of an ideal as a generalization of the multiplicity of an ideal of finite colength. We prove generalizations of various theorems involving the multiplicity of an ideal such as a principle of specialization of integral dependence, the Rees-Böger theorem, and the formula for the multiplicity of the product of two ideals. These results are applied to the study of various equisingularity conditions, such as Verdier's condition W, and conditions $A_f$ and $W_f$.

32 pages, AMSTEX 2.1/AMSPPT

Cited by in corpus (14)

• The Multiplicity-Polar Theorem
• Segre classes and invariants of singular varieties
• Multiplicity sequence and integral dependence
• Lê cycles and Milnor classes
• Equisingularity of families of hypersurfaces and applications to mappings
• Multiplicities and log canonical threshold
• Hilbert functions of multigraded algebras, mixed multiplicities of ideals and their applications
• Weak subintegral closure of ideals
• Symmetric Determinantal Singularities I: The Multiplicity of the Polar Curve
• Gap Sheaves and Vogel Cycles
• Rees's theorem for arbitrary ideals
• One parameter regularizations of products of residue currents
• Symmetric Determinantal Singularities II: Equisingularity and SEIDS
• Invariants of D(q,p) singularities