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
DOI: https://doi.org/10.1090/S1056-3911-09-00518-9
Published electronically: July 9, 2009
MathSciNet review: 2580679
Full-text PDF

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 (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

DOI: https://doi.org/10.1090/S1056-3911-09-00518-9
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

American Mathematical Society