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An analytic cancellation theorem and exotic algebraic structures on Cn

An analytic cancellation theorem and exotic algebraic structures on Cn

M. ZAINDENBERG
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  • Année : 1993
  • Tome : 217
  • Format : Électronique
  • Langue de l'ouvrage :
    Anglais
  • Pages : 251-282
  • DOI : 10.24033/ast.236

A construction of a series {Xi}i=1,2, of topologically contractible smooth complex affine algebraic surfaces of log-general type is presented. By an idea due to C.P. Ramanujam (1971), for each n3 this gives a series of exotic Cn, the affine manifolds Xi×Cn2 diffeomorphic but not biholomorphic to Cn. The following analytic concellation theorem ensures that these exotic algebraic structures are analytically different : Given a biholomorphic X×CkY×Ck where X and Y are quasiprojective varieties of log-general type, the factor Ck can be cancelled, resulting with a biregular isomorphism XY. It is also shown that none of the above exotic Cn contains a hypersurface which is the image of Cn1 under a regular injection.



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