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A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line , then ML(X×Y) = k[X]⊗ ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.
Robert Dryło. "A Remark on a Paper of Crachiola and Makar-Limanov." Bulletin of the Polish Academy of Sciences. Mathematics 59.3 (2011): 203-206. <http://eudml.org/doc/281198>.
@article{RobertDryło2011, abstract = {A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line $¹_k$, then ML(X×Y) = k[X]⊗ ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled.}, author = {Robert Dryło}, journal = {Bulletin of the Polish Academy of Sciences. Mathematics}, keywords = {Makar-Limanov invariant; additive group actions; cancellation problem}, language = {eng}, number = {3}, pages = {203-206}, title = {A Remark on a Paper of Crachiola and Makar-Limanov}, url = {http://eudml.org/doc/281198}, volume = {59}, year = {2011}, }
TY - JOUR AU - Robert Dryło TI - A Remark on a Paper of Crachiola and Makar-Limanov JO - Bulletin of the Polish Academy of Sciences. Mathematics PY - 2011 VL - 59 IS - 3 SP - 203 EP - 206 AB - A. Crachiola and L. Makar-Limanov [J. Algebra 284 (2005)] showed the following: if X is an affine curve which is not isomorphic to the affine line $¹_k$, then ML(X×Y) = k[X]⊗ ML(Y) for every affine variety Y, where k is an algebraically closed field. In this note we give a simple geometric proof of a more general fact that this property holds for every affine variety X whose set of regular points is not k-uniruled. LA - eng KW - Makar-Limanov invariant; additive group actions; cancellation problem UR - http://eudml.org/doc/281198 ER -