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Ample vector bundles and Bordiga surfaces

Antonio Lanteri, Hidetoshi Maeda

Open publisher page 3 citations

Abstract

Abstract 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 dimX – 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 (ℙ2, 𝕆 (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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What this paper is about

Abstract 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 dimX – 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 (ℙ2, 𝕆 (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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Available abstract

Abstract 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 dimX – 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 (ℙ2, 𝕆 (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)

Key concepts: Ample line bundle, Vector bundle, Mathematics, Adjunction, Tautological line bundle, Line bundle, Projective variety, Rank (graph theory)

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