Sextic variety as Galois closure variety of smooth cubic

摘要

Let V be a nonsingular projective algebraic variety of dimension n. Suppose there exists a very ample divisor D such that D~n = 6 and dim H~0 (V, O(D)) = n + 3. Then, (V, D) defines a D_6-Galois embedding if and only if it is a Galois closure variety of a smooth cubic in P~(n+1) with respect to a suitable projection center such that the pull back of hyperplane of P~n is linearly equivalent to D.