Lifting Points
The variety
#math85##tex2html_wrap_inline4496#Z(f1,…, fr)
is a subvariety of
the δ-dimensional variety, #math86##tex2html_wrap_inline4501#,
#math87#
#tex2html_wrap_indisplay4505#⊃#tex2html_wrap_indisplay4506#Z(f1,…, fr), δ = r - ρ,
defined by the polynomials
#math88#f1,…, fρ which satisfy conditions (2-3) of
Problem~#GSS#271>.
We call this sequence of polynomials a <#272#>lifting system<#272#> of
#math89##tex2html_wrap_inline4511#.
Let us now consider a new system of coordinates #math90#{Y1,…, Yr}
which is a Noether position for #math91##tex2html_wrap_inline4516# and the projection
#math92#φ : #tex2html_wrap_inline4520# #tex2html_wrap_inline4521# #tex2html_wrap_inline4524# defined by
#math93#φ(a1,…, ar) = (a1,…, aδ).
#Definition280#
#Definition300#
#Remark340#
#Proposition369#
#proof373#
#Lemma387#
#proof402#