claimroutineinferred_dep
Base algebra is a polynomial ring
Shows
identifies the base algebra as a polynomial ring
Claim·§3 The affine-space fibre and the critical point·inside thmNoncoordinate polynomial with affine three-space zero fibre
Statement (paper)
The algebra is isomorphic to , a polynomial ring in two variables, where and ; explicitly, the inverse presentation is , , , .
In plain English
The algebra is isomorphic to , with and . The inverse is given by , , , .
Why it's here
Eliminating via its defining relation turns the cusp relation into after the translation, using the identity from the previous claim. This relation is linear in , so can be eliminated and is a polynomial ring in . This explicit description lets the later claims analyse , for example the ideal , and lift the fibre presentation.
Classified routine:
This follows by substituting the earlier cusp-and-translation identity into the defining relations of B, then eliminating h and the linearly occurring variable s.