Frobenius splitting of projective toric bundles

Article

Abstract

We prove that the projectivization of the tangent bundle of a nonsingular toric variety is Frobenius split.

Keywords

Frobenius splitting toric bundles 

Mathematics Subject Classification

14M25 14G17 

Notes

Acknowledgements

The author would like to thank the referee for pointing out numerous typos, inaccuracies and mistakes and at the same time providing many helpful suggestions on improving this work.

References

  1. 1.
    Achinger P, Ilten N and Süß H, \(F\)-split and \(F\)-regular varieties with a diagonalizable group action, preprint arXiv:1503.03116 (2015) pp. 1–40
  2. 2.
    Brion M and Kumar S, Frobenius splitting methods in geometry and representation theory, Progress in Mathematics, vol. 231 (2005) (Birkhäuser)Google Scholar
  3. 3.
    Cox D A, Little J B and Schenck H K, Toric varieties (2011) (American Mathematical Society)Google Scholar
  4. 4.
    Fulton W, Introduction to toric varieties 131 (1993) (Princeton University Press)Google Scholar
  5. 5.
    Hartshorne R (1966) Residues and duality, Lecture Notes in Mathematics 20 (Berlin: Springer)Google Scholar
  6. 6.
    Hartshorne R, Algebraic geometry, 52 (1977) (Springer)Google Scholar
  7. 7.
    Hering M, Mustaţă M and Payne S, Positivity properties of toric vector bundles, Annales de L’institut Fourier 60(2) (2010) 607–640MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Klyachko A, Equivariant vector bundles on toral varieties, Math. USSR-Izv. 35 (1990) 337–375MathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Kumar S, Lauritzen N and Thomsen J F, Frobenius splitting of cotangent bundles of flag varieties, Inventiones mathematicae 136(3) (1999) 603–621MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Thomsen J F (2000) Frobenius direct images of line bundles on toric varieties, J. Algebra 226, 865–874MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Various authors, Open problems, Frobenius splitting in algebraic geometry, commutative algebra and representation theory, Conference at the University of Michigan, https://sites.google.com/site/frobeniussplitting/shedule (2010)

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.JinzhouPeople’s Republic of China

Personalised recommendations