The "canonical dimension" of an algebraic group over a field by definition isthe maximum of the canonical dimensions of principal homogenous spaces underthat group. Over a field of characteristic zero, we prove that the canonicaldimension of the projective linear group PGL_6 is 3. We give two distinctproofs, both of which rely on the birational classification of rationalsurfaces over a nonclosed field. One of the proofs involves taking a novel lookat del Pezzo surfaces of degree 6.
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机译：根据定义，场上的代数组的“规范维数”是该组下主要同质空间的规范维数的最大值。在特征为零的字段上，我们证明了射影线性群PGL_6的规范维数为3。我们给出了两个截然不同的证明，这两个证明都依赖于非封闭区域上有理曲面的双边分类。证明之一是采用新颖的6度del del Pezzo表面。
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