Detecting Flat Normal Cones Using Segre Classes
نویسنده
چکیده
Given a flat, projective morphism Y → T from an equidimensional scheme to a nonsingular curve and a subscheme Z of Y , we give conditions under which specialization of the Segre class s(NZY ) of the normal cone of Z in Y implies flatness of the normal cone. We apply this result to study when the relative tangent star cone of a flat family is flat.
منابع مشابه
Intersection Theory Class 14
1. Where we are: Segre classes of vector bundles, and Segre classes of cones 1 1.1. Segre classes of cones 1 2. What the “functoriality of Segre classes of subschemes” buys us 2 2.1. The multiplicity of a variety along a subvariety 2 3. Deformation to the normal cone 3 3.1. The construction 3 4. Specialization to the normal cone 5 4.1. Gysin pullback for local complete intersections 6 4.2. Inte...
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