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Mathematics > Algebraic Geometry

arXiv:math/0010067 (math)
[Submitted on 6 Oct 2000 (v1), last revised 31 Oct 2000 (this version, v2)]

Title:Detecting flat normal cones using Segre classes

Authors:S. J. Colley, G. Kennedy
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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.
Comments: LaTeX, 11 pages, no figures
Subjects: Algebraic Geometry (math.AG); Commutative Algebra (math.AC)
MSC classes: 13A30 14C17 (Primary) 14B25 14M05 (Secondary)
Cite as: arXiv:math/0010067 [math.AG]
  (or arXiv:math/0010067v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.math/0010067

Submission history

From: Gary Kennedy [view email]
[v1] Fri, 6 Oct 2000 22:40:02 UTC (9 KB)
[v2] Tue, 31 Oct 2000 21:19:13 UTC (9 KB)
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