Paper 2, Section II, I
Let be an algebraically closed field and . Exhibit as an open subset of affine space . Deduce that is smooth. Prove that it is also irreducible.
Prove that is isomorphic to a closed subvariety in an affine space.
Show that the matrix multiplication map
that sends a pair of matrices to their product is a morphism.
Prove that any morphism from to is constant.
Prove that for any morphism from to is constant.
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