Ample vector bundles and Bordiga surfaces | Zendy

Lanteri Antonio | Zendy; Maeda Hidetoshi | Zendy

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Ample vector bundles and Bordiga surfaces

Author(s) -

Lanteri Antonio,

Maeda Hidetoshi

Publication year - 2007

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410483

Subject(s) - ample line bundle , vector bundle , mathematics , adjunction , tautological line bundle , line bundle , projective variety , rank (graph theory) , section (typography) , locus (genetics) , bundle , combinatorics , surface (topology) , pure mathematics , zero (linguistics) , geometry , normal bundle , frame bundle , chemistry , computer science , biochemistry , materials science , linguistics , philosophy , composite material , gene , operating system

Let X be a smooth complex projective variety and let Z ⊂ X be a smooth surface, which is the zero locus of a section of an ample vector bundle ℰ of rank dim X – 2 ≥ 2 on X . Let H be an ample line bundle on X , whose restriction H Z to Z is a very ample line bundle and assume that ( Z , H Z ) is a Bordiga surface, i.e., a rational surface having (ℙ 2 , ℙ 2(4)) as its minimal adjunction theoretic reduction. Triplets ( X , ℰ, H ) as above are discussed and classified. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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