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We study the following cancellation problem over an algebraically closed field of characteristic zero. Let X, Y be affine varieties such that for some m. Assume that X is non-uniruled at infinity. Does it follow that X ≅ Y? We prove a result implying the affirmative answer in case X is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces.
Robert Dryło. "Non-uniruledness and the cancellation problem (II)." Annales Polonici Mathematici 92.1 (2007): 41-48. <http://eudml.org/doc/280158>.
@article{RobertDryło2007, abstract = {We study the following cancellation problem over an algebraically closed field of characteristic zero. Let X, Y be affine varieties such that $X × ^m ≅ Y × ^m$ for some m. Assume that X is non-uniruled at infinity. Does it follow that X ≅ Y? We prove a result implying the affirmative answer in case X is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces.}, author = {Robert Dryło}, journal = {Annales Polonici Mathematici}, keywords = {uniruled variety; cancellation problem; algebraic line bundle}, language = {eng}, number = {1}, pages = {41-48}, title = {Non-uniruledness and the cancellation problem (II)}, url = {http://eudml.org/doc/280158}, volume = {92}, year = {2007}, }
TY - JOUR AU - Robert Dryło TI - Non-uniruledness and the cancellation problem (II) JO - Annales Polonici Mathematici PY - 2007 VL - 92 IS - 1 SP - 41 EP - 48 AB - We study the following cancellation problem over an algebraically closed field of characteristic zero. Let X, Y be affine varieties such that $X × ^m ≅ Y × ^m$ for some m. Assume that X is non-uniruled at infinity. Does it follow that X ≅ Y? We prove a result implying the affirmative answer in case X is either unirational or an algebraic line bundle. However, the general answer is negative and we give as a counterexample some affine surfaces. LA - eng KW - uniruled variety; cancellation problem; algebraic line bundle UR - http://eudml.org/doc/280158 ER -