Advertisement

Fano generalized Bott manifolds

  • Yusuke SuyamaEmail author
Article
  • 13 Downloads

Abstract

We give a necessary and sufficient condition for a generalized Bott manifold to be Fano or weak Fano. As a consequence we characterize Fano Bott manifolds.

Mathematics Subject Classification

Primary 14M25 Secondary 14J45 

Notes

Acknowledgements

The author wishes to thank Professor Akihiro Higashitani for his invaluable comments. This work was supported by Grant-in-Aid for JSPS Fellows 18J00022.

References

  1. 1.
    Batyrev, V.V.: On the classification of smooth projective toric varieties. Tohoku Math. J. 43, 569–585 (1991)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Batyrev, V.V.: On the classification of toric Fano 4-folds. J. Math. Sci. (N. Y.) 94, 1021–1050 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Boyer, C.P., Calderbank, D.M.J., Tønnesen-Friedman, C.: The Kähler geometry of Bott manifolds. Adv. Math. 350, 1–62 (2019)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chary, B.N.: On Mori cone of Bott towers. J. Algebra 507, 467–501 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Choi, S., Masuda, M., Suh, D.Y.: Quasitoric manifolds over a product of simplices. Osaka J. Math. 47, 109–129 (2010)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Choi, S., Masuda, M., Suh, D.Y.: Topological classification of generalized Bott towers. Trans. Am. Math. Soc. 362, 1097–1112 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Grossberg, M., Karshon, Y.: Bott towers, complete integrability, and the extended character of representations. Duke Math. J. 76, 23–58 (1994)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hartshorne, R.: Algebraic Geometry. Graduate Texts in Math., vol. 52. Springer, New York (1977)CrossRefGoogle Scholar
  9. 9.
    Hwang, T., Lee, E., Suh, D.Y.: The Gromov width of generalized Bott manifolds. arXiv:1801.06318
  10. 10.
    Kleinschmidt, P.: A classification of toric varieties with few generators. Aequationes Math. 35, 254–266 (1988)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Oda, T.: Convex Bodies and Algebraic Geometry. An Introduction to the Theory of Toric Varieties. Ergeb. Math. Grenzgeb. (3), vol. 15. Springer, Berlin (1988)zbMATHGoogle Scholar
  12. 12.
    Park, S., Suh, D.Y.: \(\mathbb{Q}\)-trivial generalized Bott manifolds. Osaka J. Math. 51, 1081–1093 (2014)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceOsaka UniversityToyonakaJapan

Personalised recommendations