Abstract
Abstract Polarized rational surfaces (X, L) of sectional genus two ruled in conics are studied. When they are not minimal, they are described as the blow-up of đť”˝1 at some points lying on distinct fibers. Ampleness and very ampleness of L are studied in terms of their location. When L is very ample and there is a line contained in X and transverse to the fibers, the conic fibrations (X, L) are classified and a related property concerned with the inflectional locus is discussed.
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