Abstract
We prove that the projectivization of the tangent bundle of a nonsingular toric variety is Frobenius split.
Similar content being viewed by others
References
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
Brion M and Kumar S, Frobenius splitting methods in geometry and representation theory, Progress in Mathematics, vol. 231 (2005) (Birkhäuser)
Cox D A, Little J B and Schenck H K, Toric varieties (2011) (American Mathematical Society)
Fulton W, Introduction to toric varieties 131 (1993) (Princeton University Press)
Hartshorne R (1966) Residues and duality, Lecture Notes in Mathematics 20 (Berlin: Springer)
Hartshorne R, Algebraic geometry, 52 (1977) (Springer)
Hering M, Mustaţă M and Payne S, Positivity properties of toric vector bundles, Annales de L’institut Fourier 60(2) (2010) 607–640
Klyachko A, Equivariant vector bundles on toral varieties, Math. USSR-Izv. 35 (1990) 337–375
Kumar S, Lauritzen N and Thomsen J F, Frobenius splitting of cotangent bundles of flag varieties, Inventiones mathematicae 136(3) (1999) 603–621
Thomsen J F (2000) Frobenius direct images of line bundles on toric varieties, J. Algebra 226, 865–874
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)
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicating Editor: Nitin Nitsure
Rights and permissions
About this article
Cite this article
Xin, H. Frobenius splitting of projective toric bundles. Proc Math Sci 128, 8 (2018). https://doi.org/10.1007/s12044-018-0382-7
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s12044-018-0382-7