Rational surfaces and the canonical dimension of $\operatorname {\mathbf {PGL}}_6$
Rational surfaces and the canonical dimension of $\operatorname {\mathbf {PGL}}_6$
By definition, the âcanonical dimensionâ of an algebraic group over a field is the maximum of the canonical dimensions of the principal homogeneous spaces under that group. Over a field of characteristic zero, it is proved that the canonical dimension of the projective linear group $\operatorname {\mathbf {PGL}}_6$ is 3. …