Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



General isotropic flags are general (for Grassmannian Schubert calculus)

Author: Frank Sottile
Journal: J. Algebraic Geom. 19 (2010), 367-370
Published electronically: July 9, 2009
MathSciNet review: 2580679
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Abstract | References | Additional Information

Abstract: We show that general isotropic flags for odd-orthogonal and symplectic groups are general for Schubert calculus on the classical Grassmannian in that Schubert varieties defined by such flags meet transversally. This strengthens a result of Belkale and Kumar.

References [Enhancements On Off] (What's this?)

  • 1. P. Belkale and S. Kumar, Eigencone, saturation and Horn problems for symplectic and odd orthogonal groups, arXiv:0708.0398. J. Alg. Geom., to appear.
  • 2. D. Eisenbud and J. Harris, Divisors on general curves and cuspidal rational curves, Invent. Math. 74 (1983), no. 3, 371–418. MR 724011, 10.1007/BF01394242
  • 3. Wm. Fulton and P. Pragacz, Schubert varieties and degeneracy loci, Lecture Notes in Mathematics, vol. 1689, Springer-Verlag, Berlin, 1998, Appendix J by the authors in collaboration with I. Ciocan-Fontanine.
  • 4. Steven L. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287–297. MR 0360616
  • 5. E. Mukhin, V. Tarasov, and A. Varchenko, The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz, Annals of Math., to appear.
  • 6. -, Schubert calculus and representations of the general linear group, J. Amer. Math. Soc., to appear.
  • 7. Jim Ruffo, Yuval Sivan, Evgenia Soprunova, and Frank Sottile, Experimentation and conjectures in the real Schubert calculus for flag manifolds, Experiment. Math. 15 (2006), no. 2, 199–221. MR 2253007
  • 8. Frank Sottile, Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro, Experiment. Math. 9 (2000), no. 2, 161–182. MR 1780204
  • 9. Frank Sottile, Some real and unreal enumerative geometry for flag manifolds, Michigan Math. J. 48 (2000), 573–592. Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786506, 10.1307/mmj/1030132734

Additional Information

Frank Sottile
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

Received by editor(s): January 16, 2008
Received by editor(s) in revised form: July 21, 2008
Published electronically: July 9, 2009
Additional Notes: Work of Sottile supported by NSF grant DMS-0701050

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
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Online ISSN 1534-7486; Print ISSN 1056-3911
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