Advertisement

General position of points on a rational ruled surface

  • Alberto Alzati
  • Alfonso Tortora
Original Paper

Abstract

In this note we introduce a definition of general position for distinct points on a rational ruled surface and we discuss some related properties having in mind very ampleness criteria for rank 2 vector bundles.

Keywords

Rank 2 vector bundles General position Very ampleness 

Mathematics Subject Classification

Primary 14J60 Secondary 14J26 

Notes

Acknowledgements

We wish to thank A. Lanteri for fruitful conversations about our application of Theorem 11.1.2 of Beltrametti and Sommese (1995).

References

  1. Alzati, A., Besana, G.M.: Criteria for very ampleness of rank two vector bundles over ruled surfaces. Can. J. Math. 62(6), 1201–1227 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. Alzati, A., Tortora, A.: Rank 2 vector bundle over \(\mathbb{P} ^{2}(\mathbb{C})\) whose sections have special properties. Rev. Mat. Complut. 28(3), 623–654 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  3. Bazzotti, L., Casanellas, M.: Separators of points on algebraic surfaces. J. Pure Appl. Algebra 207, 316–326 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. Beltrametti, M.C., Sommese, A.J.: The adjunction theory of complex projective varieties” de Gruyter Expositions in Mathematics 16. Walter de Gruyter & Co, Berlin (1995)CrossRefGoogle Scholar
  5. Besana, G.M., Biancofiore, A.: Degree eleven projective manifolds of dimension greater than or equal to three. Forum Math. 17(5), 711–733 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  6. Bese, E.: On the spannedness and very ampleness of certain line bundles on the blow-ups of \(\mathbb{P}_{\mathbb{C}}^{2}\) and \(\mathbb{F}_{r}\). Math. Ann. 262, 225–238 (1983)MathSciNetCrossRefzbMATHGoogle Scholar
  7. Friedman, R.: Algebraic surfaces and Holomorphic Vector Bundles. Universitexts, Springer, New York (1998)CrossRefzbMATHGoogle Scholar
  8. Fania, L., Flamini, F.: Hilbert schemes of some threefold scrolls over \(\mathbb{F}_{e}\). Adv. Geom. 16(4), 413–436 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  9. Fania, L., Livorni, E.L.: Degree nine manifolds of dimension greater than or equal to 3. Math. Nachr. 169, 117–134 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  10. Fania, L., Livorni, E.L.: Degree ten manifolds of dimension n greater than or equal to 3. Math. Nachr. 188, 79–108 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  11. Griffiths, P., Harris, J.: Principles of Algebraic Geometry. Wiley Interscience Publication, New York (1994)CrossRefzbMATHGoogle Scholar
  12. Ionescu, P.: Embedded projective varieties of small invariants. In: Proceedings of the Week of Algebraic Geometry, Bucharest 1982, Lecture Notes in Mathematics, vol. 1056, pp. 142–186. Springer, New York (1984)Google Scholar
  13. Ionescu, P.: Embedded projective varieties of small invariants III. In: Algebraic Geometry, L’Aquila 1988, Lecture Notes in Mathematics, vol. 1417, pp. 138–154. Springer, New York (1990)Google Scholar

Copyright information

© The Managing Editors 2017

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniv. di MilanoMilanItaly

Personalised recommendations