Negligibility of Projective Linear Automorphisms Original Research Article

Letkbe any field,s = (aij)1 ≤ i, j ≤ n + 1 set membership, variant GLn + 1(k),K colon, equals k(x1/xn + 1,···, xn/xn + 1, y1/yn + 1,···, yn/yn + 1) a field extension of transcendence degree 2noverk. The diagonal action ofsonKis defined as [Equation] [Equation]image.There existz1,cdots, three dots, centered,zn set membership, variant Ksuch thatK = k(x1/xn + 1,···, xn/xn + 1, z1,cdots, three dots, centered,zn) ands(zi) = zifor 1 ≤ i ≤ n. In particular, ifk(x1/xn + 1,cdots, three dots, centered,xn/xn + 1)left angle bracketsright-pointing angle bracketis rational ( = purely transcendental) overk, so isKleft angle bracketsright-pointing angle bracketoverk.