Table of Contents
International Journal of Combinatorics
Volume 2013, Article ID 392437, 19 pages
http://dx.doi.org/10.1155/2013/392437
Research Article

Initial Ideals of Tangent Cones to the Richardson Varieties in the Orthogonal Grassmannian

School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India

Received 26 October 2012; Accepted 9 January 2013

Academic Editor: Nantel Bergeron

Copyright © 2013 Shyamashree Upadhyay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. P. Stanley, “Some combinatorial aspects of the Schubert calculus,” in Combinatoire et représentation du groupe symétrique, vol. 579 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1977. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. W. V. D. Hodge and D. Pedoe, Methods of Algebraic Geometry, vol. 1 of Cambridge Mathematical Library, Cambridge University Press, Cambridge, UK, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  3. K. N. Raghavan and S. Upadhyay, “Initial ideals of tangent cones to Schubert varieties in orthogonal Grassmannians,” Journal of Combinatorial Theory Series A, vol. 116, no. 3, pp. 663–683, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. B. Sturmfels, “Gröbner bases and Stanley decompositions of determinantal rings,” Mathematische Zeitschrift, vol. 205, no. 1, pp. 137–144, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  5. J. Herzog and N. V. Trung, “Gröbner bases and multiplicity of determinantal and Pfaffian ideals,” Advances in Mathematics, vol. 96, no. 1, pp. 1–37, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. V. Kodiyalam and K. N. Raghavan, “Hilbert functions of points on Schubert varieties in Grassmannians,” Journal of Algebra, vol. 270, no. 1, pp. 28–54, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. V. Kreiman and V. Lakshmibai, Monomial bases and applications for Richardson and Schubert varieties in ordinary and affine Grassmannians [Ph.D. thesis], Northeastern University, 2003.
  8. V. Kreiman, “Local properties of Richardson varieties in the Grassmannian via a bounded Robinson-Schensted-Knuth correspondence,” Journal of Algebraic Combinatorics, vol. 27, no. 3, pp. 351–382, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. K. N. Raghavan and S. Upadhyay, “Hilbert functions of points on Schubert varieties in orthogonal Grassmannians,” Journal of Algebraic Combinatorics, vol. 31, no. 3, pp. 355–409, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. V. Lakshmibai and C. S. Seshadri, “Geometry of G/P—II. The work of de Concini and Procesi and the basic conjectures,” Proceedings of the Indian Academy of Sciences A, vol. 87, no. 2, pp. 1–54, 1978. View at Google Scholar · View at MathSciNet