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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-2,
author = {Robert Dry\l o},
title = {A Remark on a Paper of Crachiola and Makar-Limanov},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {59},
year = {2011},
pages = {203-206},
zbl = {1231.13007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-2}
}
Robert Dryło. A Remark on a Paper of Crachiola and Makar-Limanov. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 59 (2011) pp. 203-206. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba59-3-2/