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On the reducibility of characteristic varieties

Author: Tom Braden
Journal: Proc. Amer. Math. Soc. 130 (2002), 2037-2043
MSC (2000): Primary 32S60; Secondary 32S30
Published electronically: February 12, 2002
MathSciNet review: 1896039
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Abstract: We show that some monodromies in the Morse local systems of a conically stratified perverse sheaf imply that other Morse local systems for smaller strata do not vanish. This result is then used to explain the examples of reducible characteristic varieties of Schubert varieties given by Kashiwara and Saito in type $A$ and by Boe and Fu for the Lagrangian Grassmannian.

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

  • 1. B. Boe and J. Fu, Characteristic cycles associated to Schubert varieties in classical Hermitian symmetric spaces, Canad. J. Math. 49 (1997), 417-467. MR 98j:14068
  • 2. T. Braden, Characteristic cycles of toric varieties; perverse sheaves on rank stratifications, MIT Ph.D. thesis, 1995.
  • 3. -, Perverse sheaves on Grassmannians, preprint math.AG/9907152, to appear in Canadian J. Math.
  • 4. T. Braden and M. Grinberg, Perverse sheaves on rank stratifications, Duke Math. J. 96 (1999), 317-362. MR 2000f:14031
  • 5. I. Gel'fand, M. Kapranov, and A. Zelevinsky, Discriminants, resultants, and multidimensional determinants, Birkhäuser, 1994. MR 95e:14045
  • 6. M. Goresky and R. MacPherson, Stratified Morse Theory, Springer 1988. MR 90d:57039
  • 7. M. Kashiwara and Y. Saito, Geometric construction of crystal bases, Duke Math. J. 89 (1997), 9-36. MR 99e:17025
  • 8. M. Kashiwara and P. Schapira, Sheaves on Manifolds, Springer 1990. MR 92a:58132
  • 9. D. Kazhdan and G. Lusztig, A topological approach to Springer's representations, Adv. Math. 38 (1980), 222-228. MR 82f:20076
  • 10. R. D. MacPherson and K. Vilonen, Elementary construction of perverse sheaves, Inv. Math. 84 (1986), 403-435. MR 87m:32028
  • 11. C. Sabbah, Quelques remarques sur la géométrie des espaces conormaux, Astérisque 130, 1985, 161-192. MR 87f:32031
  • 12. T. Tanisaki, Characteristic varieties of highest weight modules and primitive quotients, in ``Representations of Lie groups, Kyoto, Hiroshima 1986'', Adv. Stud. Pure Math. 14, Acad. Press 1988, pp. 1-30. MR 91b:17014
  • 13. J-L. Verdier, Prolongement des Faisceaux Pervers Monodromiques, Astérisque 130 (1985) 218-236. MR 87d:32019

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Additional Information

Tom Braden
Affiliation: Department of Mathematics and Statistics, University of Massachusetts–Amherst, Amherst, Massachusetts 01003

Keywords: Perverse sheaves, vanishing cycles, Morse group, characteristic variety
Received by editor(s): February 27, 2000
Received by editor(s) in revised form: January 29, 2001
Published electronically: February 12, 2002
Communicated by: Michael Stillman
Article copyright: © Copyright 2002 American Mathematical Society