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Mathematische Annalen

, Volume 358, Issue 1–2, pp 465–476 | Cite as

Seshadri constants and degrees of defining polynomials

  • Atsushi Ito
  • Makoto Miura
Article
  • 176 Downloads

Abstract

In this paper, we study a relation between Seshadri constants and degrees of defining polynomials. In particular, we compute the Seshadri constants on Fano varieties obtained as complete intersections in rational homogeneous spaces of Picard number one.

Mathematics Subject Classification (1991)

14C20 

Notes

Acknowledgments

The authors would like to express their gratitude to Professor Yujiro Kawamata for his valuable advice, comments, and warm encouragement. They are also grateful to Professors Katsuhisa Furukawa and Kiwamu Watanabe for their useful comments and suggestions.

References

  1. 1.
    Bauer, T.: Seshadri constants on algebraic surfaces. Math. Ann. 313(3), 547–583 (1999)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Chan, K.: A lower bound on Seshadri constants of hyperplane bundles on threefolds. Math. Z. 264(3), 497–505 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Debarre, O.: Higher-dimensional algebraic geometry, Universitext, pp. xiv+233. Springer, New York (2001)Google Scholar
  4. 4.
    Demailly, J.P.: Singular Hermitian metrics on positive line bundles, complex algebraic varieties (Bayreuth, 1990), Lecture Notes in Math., vol. 1507, pp. 87–104. Springer, Berlin (1992)Google Scholar
  5. 5.
    Hwang, J.-M.: On the degrees of Fano four-folds of Picard number \(1\). J. Reine Angew. Math. 556, 225–235 (2003)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Ito, A.: Seshadri constants via toric degenerations. J. Reine Angew. Math. doi: 10.1515/crelle-2012-0116 (2012, to appear)
  7. 7.
    Kollár, J.: Rational curves on algebraic varieties, Ergeb. Math. Grenzgeb. (3), vol. 32, Springer, Berlin (1996)Google Scholar
  8. 8.
    Lazarsfeld, R.: Positivity in algebraic geometry I, Ergebnisse der Mathematik undihrer Grenzgebiete, vol. 48. Springer, Berlin (2004)Google Scholar
  9. 9.
    Lichtenstein, W.: A system of quadrics describing the orbit of the highest weight vector. Proc. Amer. Math. Soc. 84(4), 605–608 (1982)CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Mumford, D.: Varieties defined by quadratic equations, 1970 Questions on Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 29–100 Edizioni Cremonese, Rome (1969)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoMeguroJapan

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