Factorial threefolds with Ga-actions
نویسندگان
چکیده
The affine cancellation problem, which asks whether complex affine varieties with isomorphic cylinders are themselves isomorphic, has a positive solution for two dimensional varieties whose coordinate rings are unique factorization domains, in particular for C, but counterexamples are found within normal surfaces (Danielewski surfaces) and factorial threefolds of logarithmic Kodaira dimension equal to 1. The latter are therefore remote from C, the first unknown case where the base of one cylinder is an affine space. Locally trivial Ga-actions play a significant role in these examples. Factorial threefolds admitting free Ga-actions are discussed, especially a class of varieties with negative logarithmic Kodaira dimension which are total spaces of nonisomorphic Ga-bundles. Some members of the class are shown to be isomorphic as abstract varieties, but it is unknown whether any members of the class constitute counterexamples to cancellation.
منابع مشابه
The Automorphism Group of Certain Factorial Threefolds and a Cancellation Problem
The automorphism groups of certain factorial complex affine threefolds admitting locally trivial actions of the additive group are determined. As a consequence new counterexamples to a generalized cancellation problem are obtained.
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