84
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Gale duality and homogeneous toric varieties

Pages 3539-3552 | Received 13 Apr 2017, Published online: 08 Feb 2018

References

  • Arzhantsev, I., Bazhov, I. (2013). On orbits of the automorphism group on an affine toric variety. Central Eur. J. Math. 11(10):1713–1724.
  • Arzhantsev, I., Derenthal, U., Hausen, J., Laface, A. (2015). Cox Rings, Cambridge Studies in Advanced Mathematics, Vol. 144. New York: Cambridge University Press.
  • Arzhantsev, I., Gaifullin, S. (2010). Homogeneous toric varieties. J. Lie Theory 20(2):283–293.
  • Arzhantsev, I., Hausen, J. (2006). On embeddings of homogeneous spaces with small boundary. J. Algebra 304(2):950–988.
  • Arzhantsev, I., Hausen, J., Herppich, E., Liendo, A. (2014). The automorphism group of a variety with torus action of complexity one. Moscow Math. J. 14(3):429–471.
  • Arzhantsev, I., Kotenkova, P. (2015). Equivariant embeddings of commutative linear algebraic groups of corank one. Documenta Math. 20:1039–1053.
  • Arzhantsev, I., Kuyumzhiyan, K., Zaidenberg, M. (2012). Flag varieties, toric varieties, and suspensions: Three instances of infinite transitivity. Sbornik: Math. 203(7):923–949.
  • Bazhov, I. (2013). On orbits of the automorphism group on a complete toric variety. Beiträge zur Algebra und Geometrie 54(2):471–481.
  • Berchtold, F., Hausen, J. (2004). Bunches of cones in the divisor class group - A new combinatorial language for toric varieties. Int. Math. Res. Notices 2004(6):261–302.
  • Cox, D. (1995). The homogeneous coordinate ring of a toric variety. J. Algebra Geom. 4(1):17–50.
  • Cox, D., Little, J., Schenck, H. (2011). Toric Varieties, Graduate Studies in Mathematics, Vol. 124. Providence, RI: American Mathematical Society.
  • Demazure, M. (1970). Sous-groupes algebriques de rang maximum du groupe de Cremona. Ann. Sci. Ecole Norm. Sup. 3:507–588.
  • Dubouloz, A. (2009). The cylinder over the Koras-Russell cubic threefold has a trivial Makar-Limanov invariant. Transform. Groups 14(3):531–539.
  • Fulton, W. (1993). Introduction to Toric Varieties, Annals of Mathematics Studies, Vol. 131. Princeton, NJ: Princeton University Press.
  • Liendo, A. (2010). 𝔾a-actions of fiber type on affine đť•‹-varieties. J. Algebra 324(12):3653–3665.
  • Nill, B. (2006). Complete toric varieties with reductive automorphism group. Math. Z. 252(4):767–786.
  • Oda, T. (1988). Convex Bodies and Algebraic Geometry: An Introduction to Toric Varieties, A Series of Modern Surveys in Mathematics, Vol. 15. Berlin: Springer Verlag.
  • Oda, T., Park, H. S. (1991). Linear Gale transforms and Gel’fand-Kapranov-Zelevinskij decompositions. Linear Gale transforms and Gel’fand-Kapranov-Zelevinskij decompositions (2) 43(3):375–399.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.