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The threefold containing the Bordiga surface of degree ten as a hyperplane section

Published online by Cambridge University Press:  01 November 2008

HIDETOSHI MAEDA*
Affiliation:
Department of Mathematics, Faculty of Science and Engineering, Waseda University, 3-4-1 Ohkubo, Shinjuku-ku, Tokyo 169-8555, Japan. e-mail: maeda@variety.sci.waseda.ac.jp

Abstract

Let be a very ample vector bundle of rank 2 on with c1() = 4 and c2() = 6. Then it is proved that is the cokernel of a bundle monomorphism , where is the tangent bundle of . This gives a new example of a threefold containing a Bordiga surface as a hyperplane section.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2008

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References

REFERENCES

[I1]Ionescu, P. Embedded projective varieties of small invariants. Algebraic Geometry (Bucharest, 1982) (ed. L. Bǎdescu and D. Popescu). Lecture Notes in Math. 1056 (Springer, 1984), pp.142–186.Google Scholar
[I2]Ionescu, P. Embedded projective varieties of small invariants. III. Algebraic Geometry (L'Aquila, 1988) (ed. A. J. Sommese, A. Biancofiore and E. L. Livorni). Lecture Notes in Math. 1417 (Springer, 1990), pp. 138–154.Google Scholar
[LM]Lanteri, A. and Maeda, H.Projective manifolds of sectional genus three as zero loci of sections of ample vector bundles. Math. Proc. Camb. Phil. Soc. 144 (2008), 109118.Google Scholar
[MM]Mori, S. and Mukai, S.Classification of Fano 3-folds with B_2 ≥ 2. Manuscripta Math. 36 (1981), 147162; Erratum. Manuscripta Math. 110 (2003), 407.Google Scholar
[OSS]Okonek, C., Schneider, M. and Spindler, H.Vector bundles on complex projective spaces. Progr. Math. 3 (Birkhäuser Boston, 1980).CrossRefGoogle Scholar