Rank 2 vector bundles over $${\mathbb {P}}^{2}(\mathbb {C})$$ whose sections vanish on points in general position
Tóm tắt
In this paper we address the classification of rank 2 vector bundles
$$E,$$
over
$${\mathbb {P}}^{2}(\mathbb {C}),$$
such that the zero locus of a general section of
$$E$$
is a set of distinct points in general position. We also discuss the existence of smooth threefolds
$$X={\mathbb {P}}(E),$$
arising from such bundles.
Tài liệu tham khảo
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)
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)
Besana, G.M., Biancofiore, A.: Degree eleven projective manifolds of dimension greater than or equal to three. Forum Math. 17(5), 711–733 (2005)
Ellia, P.: Chern classes of rank two globally generated vector bundles on \({\mathbb{P}}^{2}\). Rend. Lincei Mat. Appl. 24, 147–163 (2013)
Friedman, R.: Algebraic Surfaces and Holomorphic Vector Bundles. Universitexts, Springer-Verlag, New York (1998)
Fania, L., Livorni, E.L.: Degree nine manifolds of dimension greater than or equal to 3. Math. Nachr. 169, 117–134 (1994)
Fania, L., Livorni, E.L.: Degree ten manifolds of dimension n greater than or equal to 3. Math. Nachr. 188, 79–108 (1997)
Griffiths, P., Harris, J.: Principles of Algebraic Geometry. Wiley Interscience Publication, New York (1994)
Ionescu, P.: Embedded projective varieties of small invariants. In: Proceedings of the Week of Algebraic Geometry, Bucharest 1982, pp. 142–186. Springer Lectures Notes in Mathematics 1056 (1984)
Ionescu, P.: Embedded projective varieties of small invariants III. In: Algebraic Geometry, L’Aquila 1988, pp. 138–154. Springer Lectures Notes in Mathematics 1417, (1990)
Kleiman, S.: Bertini and his two fundamental theorems. Rend. Circ. Mat. Palermo 55(2), 9–37 (1998)
Lazarsfeld, R.: Lectures on linear series (with the assistance of Guillermo Fernández del Busto). IAS, Park City Math. Ser., 3, Complex algebraic geometry (Park City, UT, 1993), pp. 161–219, Amer. Math. Soc., Providence, RI (1997)
Mumford, D.: Lectures on Curves on An Algebraic Surface. Ann. Math. Studies 59. Princeton University Press, New Jersey (1996)
Okonek, C., Schneider, M., Spindler, H.: Vector Bundles on Complex Projective Spaces. Birkhäuser/Springer Basel AG, Basel (2011)