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Detecting flat normal cones using Segre classes
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classification
math.AGmath.AC
keywords
flatconenormalsegreapplyclassclassesconditions
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abstract
Given a flat, projective morphism $Y \to T$ from an equidimensional scheme to a nonsingular curve and a subscheme $Z$ of $Y$, we give conditions under which specialization of the Segre class $s(N_{Z}Y)$ 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.
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