Detecting flat normal cones using Segre classes

Details Detecting flat normal cones using Segre classes Detecting flat normal cones using Segre classes

2000-10-06

arxiv.org/abs/math/0010067v2

Mathematics

Algebraic Geometry

LaTeX, 11 pages, no figures

Scientific paper

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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