A quasi-smooth well-formed complete intersection log del Pezzo surface of index one admits an anticanonical polar cylinder if and only if it is the complete intersection of two quadrics in P4.
Math., 152 (2016), pp
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Rigid affine cones over singular del Pezzo surfaces
A quasi-smooth well-formed complete intersection log del Pezzo surface of index one admits an anticanonical polar cylinder if and only if it is the complete intersection of two quadrics in P4.