Rational conic fibrations of sectional genus two
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Antonio Lanteri
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 đœ1 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.
Acknowledgements
The authors are grateful to the referee for useful remarks. The first author is a member of G.N.S.A.G.A. of the Italian INdAM. He would like to thank the PRIN 2015 Geometry of Algebraic Varieties and the University of Milano for partial support. The second author wants to thank the Spanish Ministry of Science, Innovation and Universities (Project MTM 2015-65968-P âGeometrĂa algebraica y analĂtica y aplicacionesâ).
Communicated by: R. Cavalieri
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Complex geodesics in convex domains and â-convexity of semitube domains
- Triharmonic Riemannian submersions from 3-dimensional space forms
- Ricci almost solitons and contact geometry
- Shapes of centrally symmetric octahedra with prescribed cone-deficits
- Equivariant Ulrich bundles on exceptional homogeneous varieties
- Exotic Steiner chains in Miquelian Möbius planes of odd order
- Double cover K3 surfaces of Hirzebruch surfaces
- The dual cone of sums of non-negative circuit polynomials
- Einstein tori and crooked surfaces
- Compact null hypersurfaces in Lorentzian manifolds
- Hyperbolic torsion polynomials of pretzel knots
- Geodesic orbit Randers metrics on spheres
- Rational conic fibrations of sectional genus two
- Hodge numbers of hypersurfaces in â4 with ordinary triple points
Artikel in diesem Heft
- Frontmatter
- Complex geodesics in convex domains and â-convexity of semitube domains
- Triharmonic Riemannian submersions from 3-dimensional space forms
- Ricci almost solitons and contact geometry
- Shapes of centrally symmetric octahedra with prescribed cone-deficits
- Equivariant Ulrich bundles on exceptional homogeneous varieties
- Exotic Steiner chains in Miquelian Möbius planes of odd order
- Double cover K3 surfaces of Hirzebruch surfaces
- The dual cone of sums of non-negative circuit polynomials
- Einstein tori and crooked surfaces
- Compact null hypersurfaces in Lorentzian manifolds
- Hyperbolic torsion polynomials of pretzel knots
- Geodesic orbit Randers metrics on spheres
- Rational conic fibrations of sectional genus two
- Hodge numbers of hypersurfaces in â4 with ordinary triple points
