Detecting flat normal cones using Segre classes

Authors
Colley, SJ Kennedy, G
Citation
Sj. Colley et G. Kennedy, Detecting flat normal cones using Segre classes, J ALGEBRA, 245(1), 2001, pp. 182-192
Citations number
11
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF ALGEBRA
ISSN journal
00218693 → ACNP
Volume
245
Issue
1
Year of publication
2001
Pages
182 - 192
Database
ISI
SICI code
0021-8693(20011101)245:1<182:DFNCUS>2.0.ZU;2-M
Abstract
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 impl ies flatness of the normal cone. We apply this result to study when the rel ative tangent star cone of a flat family is flat. (C) 2001 Academic Press.