JORDAN PROPERTIES OF AUTOMORPHISM GROUPS OF CERTAIN OPEN ALGEBRAIC VARIETIES

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Let W be a quasiprojective variety over an algebraically closed field of characteristic zero. Assume that W is birational to a product of a smooth projective variety A and the projective line. We prove that if A contains no rational curves then the automorphism group G := Aut (W) of W is Jordan. That means that there is a positive integer J = J (W) such that every finite subgroup ℬ of G contains a commutative subgroup $$ \mathcal{A} $$ such that $$ \mathcal{A} $$ is normal in ℬ and the index $$ \left[\mathrm{\mathcal{B}}:\mathcal{A}\right]\le J $$ .