An open subset in a normal projective variety X is called a cylinder if it is isomorphic to A1 × Z for some affine variety Z. With an effective condition on the boundary of the cylinder, this A1-ruledness ensures that a nontrivial unipotent group action on the affine cone of the corresponding ample polarization (X, H). In particular, for del Pezzo surfaces, there are good properties to determine its ample polar cylindricity. Here we will remark on some results for del Pezzo surfaces known so far containing recent own research in progress. We consider smooth case only and work over an algebraically closed field of characteristic zero.

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