561 research outputs found
Log-uniruled affine varieties without cylinder-like open subsets
A classical result of Miyanishi-Sugie and Keel-McKernan asserts that for
smooth affine surfaces, affine-uniruledness is equivalent to affine-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 exists smooth affine varieties which are affine-uniruled but not
affine-ruled
Unipotent Group Actions on Del Pezzo Cones
In a previous paper we established that for any del Pezzo surface Y of degree
at least 4, the affine cone X over Y embedded via a pluri-anticanonical linear
system admits an effective Ga-action. In particular, the group Aut(X) is
infinite dimensional. In contrast, we show in this note that for a del Pezzo
surface Y of degree at most 2 the generalized cones X as above do not admit any
non-trivial action of a unipotent algebraic group.Comment: 10p.; a reference added; minor change
Ga-actions on affine cones
We give a criterion of existence of a unipotent group action on the affine
cone over a projective variety or, more generally, on the affine quasicone over
a variety which is projective over another affine variety.Comment: 16p. In a formula in the proof of Lemma 2.3, the direct sum was
replaced by the usual sum . The authors are grateful to Kevin Langlois for
mentioning this inaccurac
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