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General isotropic flags are general (for Grassmannian Schubert calculus)
Author(s):
Frank
Sottile
Journal:
J. Algebraic Geom.
Posted:
July 9, 2009
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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:
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- 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 (85h:14019)
- 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.
- S. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287-297. MR 0360616 (50:13063)
- 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.
- J. Ruffo, Y. Sivan, E. Soprunova, and F. Sottile, Experimentation and conjectures in the real Schubert calculus for flag manifolds, Experiment. Math. 15 (2006), no. 2, 199-221. MR 2253007 (2007g:14066)
- 8.
- F. Sottile, Real Schubert calculus: polynomial systems and a conjecture of Shapiro and Shapiro, Experiment. Math. 9 (2000), no. 2, 161-182. MR 1780204 (2001e:14054)
- 9.
- -, 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 (2002d:14085)
Additional Information:
Frank
Sottile
Affiliation:
Department of Mathematics, Texas A\&M University, College Station, Texas 77843
Email:
sottile@math.tamu.edu
PII:
S 1056-3911(09)00518-9
Received by editor(s):
January 16, 2008
Received by editor(s) in revised form:
July 21, 2008
Posted:
July 9, 2009
Additional Notes:
Work of Sottile supported by NSF grant DMS-0701050
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