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 _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.
Rational conic fibrations sectional genus two / A. Lanteri, R. Mallavibarrena. - In: ADVANCES IN GEOMETRY. - ISSN 1615-715X. - 21:2(2021 May), pp. 281-292. [10.1515/advgeom-2020-0022]
Rational conic fibrations sectional genus two
A. LanteriPrimo
;
2021
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 _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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