Negligibility of Projective Linear Automorphisms
Journal
Journal of Algebra
Journal Volume
199
Journal Issue
1
Pages
344-366
Date Issued
1998
Author(s)
Abstract
Letkbe any field,s=(aij)1≤i,j≤n+1∈GL n+1(k),Kk(x1/x n+1,···,xn/xn+1,y 1/yn+1,···,yn/y n+1) a field extension of transcendence degree 2noverk. The diagonal action ofsonKis defined as [Equation] [Equation]THEOREM.There existz1,zn∈Ksuch thatK=k(x1/xn+1,···,x n/xn+1,z1,zn) ands(zi)=zifor 1≤i≤n. In particular, ifk(x1/xn+1,xn/xn+1) 〈s〉is rational (=purely transcendental) overk, so isK〈s〉overk. © 1998 Academic Press.
Type
journal article