no. 2
Log-uniruled affine varieties without cylinder-like open subsets
[Variétés affines log-uniréglées ne contenant pas d'ouverts cylindriques]
Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 383-401

A classical result of Miyanishi-Sugie and Keel-McKernan asserts that for smooth affine surfaces, 𝔸1-uniruledness is equivalent to 𝔸1-ruledness, both properties being in fact equivalent to the negativity of the logarithmic Kodaira dimension. Here we show in contrast that starting from dimension three, there exist smooth affine varieties which are 𝔸1-uniruled but not 𝔸1-ruled.

D'après une caractérisation due à Miyanishi-Sugie et Keel-McKernan, une surface affine lisse S est 𝔸1-uniréglée si et seulement si elle est 𝔸1-réglée, ces deux propriétés étant en fait équivalentes à la négativité de la dimension de Kodaira logarithmique de S. Nous montrons dans cet article que cette équivalence ne subsiste pas en dimension supérieure ou égale à trois.

Publié le :
DOI : 10.24033/bsmf.2692
Classification : 14J50, 14R25, 14D06, 14E08
Keywords: log-uniruled varieties, affine ruled varieties, cylindrical open subset, additive group actions.
Mots-clés : Variétés log-uniréglées, variétés affine-réglées, ouverts cylindriques, actions de groupes additifs. 
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     title = {Log-uniruled affine varieties without cylinder-like open subsets},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {383--401},
     year = {2015},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {143},
     number = {2},
     doi = {10.24033/bsmf.2692},
     mrnumber = {3351185},
     zbl = {1327.14196},
     language = {en},
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Dubouloz, Adrien; Kishimoto, Takashi. Log-uniruled affine varieties without cylinder-like open subsets. Bulletin de la Société Mathématique de France, Tome 143 (2015) no. 2, pp. 383-401. doi: 10.24033/bsmf.2692

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