A Remark on a Paper of Crachiola and Makar-Limanov

Volume 59 / 2011

Robert Dryło Bulletin Polish Acad. Sci. Math. 59 (2011), 203-206 MSC: 13A50, 14R10, 14R20. DOI: 10.4064/ba59-3-2


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.


  • Robert DryłoInstytut Matematyczny PAN
    Śniadeckich 8
    00-956 Warszawa, Poland
    Instytut Matematyki
    Uniwersytet Jana Kochanowskiego w Kielcach
    Świętokrzyska 15
    25-406 Kielce, Poland

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