Finite determinacy and topological triviality. II : sufficient conditions and topological stability
A Bezout theorem for determinantal modules
A Topological Invariant for Stable Map Germs.
Finite Determinacy and Topological Triviality I.
On the Pham example and the universal topological stratification of singularities
The versality discriminant and local topological equivalence of mappings
We will extend the infinitesimal criteria for the equisingularity (i.e. topological triviality) of deformations of germs of mappings , , to non-finitely determined germs (these occur generically outside the “nice dimensions” for Mather, even among topologically stable mappings). The failure of finite determinacy is described geometrically by the “versality discriminant”, which is the set of points where is not stable (i.e. viewed as an unfolding it is not versal). The criterion asserts that...
Topological triviality of versal unfoldings of complete intersections
We obtain algebraic and geometric conditions for the topological triviality of versal unfoldings of weighted homogeneous complete intersections along subspaces corresponding to deformations of maximal weight. These results are applied: to infinite families of surface singularities in which begin with the exceptional unimodular singularities, to the intersection of pairs of generic quadrics, and to certain curve singularities. The algebraic conditions are related to the operation of...
Smoothness and geometry of boundaries associated to skeletal structures I: sufficient conditions for smoothness
We introduce a skeletal structure in , which is an - dimensional Whitney stratified set on which is defined a multivalued “radial vector field” . This is an extension of notion of the Blum medial axis of a region in with generic smooth boundary. For such a skeletal structure there is defined an “associated boundary” . We introduce geometric invariants of the radial vector field on and a “radial flow” from to . Together these allow us to provide sufficient numerical conditions for...
A-Codimension and the vanishing topology of discriminants.
Topological Triviality of Deformations of Functions and Newton Filtrations.
On the Hilbert-Samuel partition of stable map-germs
Universal topological stratification for the Pham example
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