A Remark on a Paper of Crachiola and Makar-Limanov
Volume 59 / 2011
Bulletin Polish Acad. Sci. Math. 59 (2011), 203-206
MSC: 13A50, 14R10, 14R20.
DOI: 10.4064/ba59-3-2
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 $\mathbb A^1_k$, then $\mathop{\rm ML}(X\times Y)=k[X]\otimes \mathop{\rm ML}(Y)$ 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.
