Manuscript XIV-G@1 · XIV-G.tex · section · 791c6644

One ambient space and one characteristic test locus

G2: the chosen locus and the relation audit › One ambient space and one characteristic test locus · lines 929–965

XIV-G@1#eq:chosenN

All common-kernel statements take place in

W = A \times B \times Z \times Y, dim W = 16,

in the order $(a, b, z, y)$ .

For the characteristic test in this paper, choose

N = N_{att} = N_{att} \cap D_{obs} .

It has codimension eight in $W$ . The residual metric variable is not projected out.

The numerical stratum $N^{\circ}$ has codimension four in the three-vertex space. Its full lift $N_{att}$ also has codimension four, with $z$ free. Neither is substituted for (eq:chosenN) in a degree statement. No characteristic degree is assigned to any of them.

Let

d = a - z .

At $w \in N$ , define the already copied oriented conormals

n_{R} = - \frac{d q _{R}}{2 β}, n_{1} = \frac{d q _{1}}{2 α}, n_{2} = \frac{d q _{2}}{2 ( β - α )} .

They satisfy

n_{R} + n_{1} + n_{2} = 0.

Displayed formulas in this passage

XIV-G@1#eq:chosenN · line 938
$N = N_{att} = N_{att} \cap D_{obs} .$
unlabeled · line 932
$W = A \times B \times Z \times Y, dim W = 16,$
unlabeled · line 952
$d = a - z .$
unlabeled · line 956
$n_{R} = - \frac{d q _{R}}{2 β}, n_{1} = \frac{d q _{1}}{2 α}, n_{2} = \frac{d q _{2}}{2 ( β - α )} .$
unlabeled · line 962
$n_{R} + n_{1} + n_{2} = 0.$