Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

THE MAIN COMPONENT OF A REDUCIBLE HILBERT CURVE OF CONIC FIBRATIONS

  • Received : 2020.09.19
  • Accepted : 2021.07.05
  • Published : 2021.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

The study of reducible Hilbert curves of conic fibrations over a smooth surface is carried on in this paper and the question of when the main component is itself the Hilbert curve of some ℚ-polarized surface is dealt with. Special attention is paid to the polynomial defining the canonical equation of the Hilbert curve.

Keywords

References

  1. W. P. Barth, K. Hulek, C. A. M. Peters, and A. Van de Ven, Compact complex surfaces, second edition, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, 4, Springer-Verlag, Berlin, 2004. https://doi.org/10.1007/978-3-642-57739-0
  2. M. Beltrametti, A. Lanteri, and M. Palleschi, Algebraic surfaces containing an ample divisor of arithmetic genus two, Ark. Mat. 25 (1987), no. 2, 189-210. https://doi.org/10.1007/BF02384443
  3. M. C. Beltrametti, A. Lanteri, and A. J. Sommese, Hilbert curves of polarized varieties, J. Pure Appl. Algebra 214 (2010), no. 4, 461-479. https://doi.org/10.1016/j.jpaa.2009.06.009
  4. F. A. Bogomolov, Holomorphic tensors and vector bundles on projective manifolds, Izv. Akad. Nauk SSSR Ser. Mat. 42 (1978), no. 6, 1227-1287, 1439.
  5. M. L. Fania and A. Lanteri, Hilbert curves of conic fibrations over smooth surfaces, Comm. Algebra 49 (2021), no. 2, 545-566. https://doi.org/10.1080/00927872.2020.1807022
  6. T. Fujita, Classification theories of polarized varieties, London Mathematical Society Lecture Note Series, 155, Cambridge University Press, Cambridge, 1990. https://doi.org/10.1017/CBO9780511662638
  7. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, No. 52, Springer-Verlag, New York, 1977.
  8. A. Lanteri, Characterizing scrolls via the Hilbert curve, Internat. J. Math. 25 (2014), no. 11, 1450101, 17 pp. https://doi.org/10.1142/S0129167X14501018
  9. A. Lanteri, Hilbert curves of 3-dimensional scrolls over surfaces, J. Pure Appl. Algebra 222 (2018), no. 1, 139-154. https://doi.org/10.1016/j.jpaa.2017.03.008
  10. A. Lanteri and A. L. Tironi, Hilbert curve characterizations of some relevant polarized manifolds, arXiv: 1803.01131, 2018.
  11. H. Maeda, On polarized surfaces of sectional genus three, Sci. Papers College Arts Sci. Univ. Tokyo 37 (1988), no. 2, 103-112.
  12. K. Yokoyama, On blowing-up of polarized surfaces, J. Math. Soc. Japan 51 (1999), no. 3, 523-533. https://doi.org/10.2969/jmsj/05130523