Advanced search
Publication Cover
Communications in Algebra Volume 31, 2003 - Issue 7
Submit an article Journal homepage
46
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Combinatorial Tangent Space and Rational Smoothness of Schubert Varieties

Stéphane Gaussent Department of Mathematics, University of Aarhus, Ny Munkegade, Denmark; Department of Mathematics, University of Aarhus, 8000 Aarhus C, Ny Munkegade, DenmarkCorrespondence[email protected]
Pages 3111-3133 | Received 01 Oct 2000, Published online: 31 Aug 2006

References

  • Bourbaki , N. 1986 . Groupes et algèbre de Lie , Chapitres 4,5 et 6 Paris : Hermann .
  • Carrell , J. B. 1994 . The Bruhat graph of a Coxeter group,a conjecture of Deodhar,and rational smoothness of Schubert varieties . Proc. Symp. in Pure Math. , 56 ( Part I ) : 53 – 61 .
  • Carrell , J. B. 1995 . On the smooth points of a Schubert variety . Cand. Math. Soc. Conf. Proc. , 16 : 15 – 33 .
  • Carrell , J. B. 1997 . “ The span of the tangent cone of a Schubert variety ” . In Algebraic Groups and Lie Groups , Soc. Lectures Series 9 51 – 60 . Cambridge University Press .
  • Contou-Carrère,C. (1983). Géométrie des Groupes Semi-Simples,Résolutions équivariantes et Lieu Singulier de Leurs Variétés de Schubert. Thèse d’état,Université Montpellier II (published partly as,Le Lieu singulier des variétés de Schubert (1988). Adv. Math.,71:186–221)
  • Demazure , M. 1974 . Désingularisation des variétés de schubert . Ann. Sci. Ecole Norm. Sup. , 7 ( 4 ) : 53 – 88 .
  • Deodhar , V. 1985 . Local poincaré duality and non singularity of Schubert varieties . Comm. Algebra , 13 ( 6 ) : 1379 – 1388 .
  • Deodhar , V. 1990 . A combinatorial setting for question in Kazhdan-Susztig theory . Geometriae Dedicata , 36 : 95 – 119 .
  • Deodhar , V. 1991 . A brief survey of Kazhdan-Lusztig theory and related topics . Proc. Symp. in Pure Math. , 56 ( Part I ) : 105 – 124 .
  • Gaussent,S. (2001a) Etude de la résolution de Bott-Samelson d'une variété de Schubert,en vue d'un critère valuatif de lissité. Ph.D. thesis,Université Montpellier 2
  • Gaussent , S. 2001b . The fibre of the Bott-Samelson resolution . Indag. Math. N.S. , 12 ( 4 ) : 453 – 468 .
  • Grothendieck , A. and Demazure , M. 1970 . Schémas en Groupes I,II,III , Lectures notes in Math. 151,152,153 Heidelberg : Springer-Verlag .
  • Hansen , H. C. 1973 . On cycles of flag manifolds . Math. Scand. , 33 : 269 – 274 .
  • Kazhdan , D. and Lusztig , G. 1979 . Representation of Coxeter groups and Hecke algebras . Invent. Math. , 53 : 165 – 184 .
  • Mathieu , O. 1988 . Formules de caractères pour les algèbres de Kac-Moody générales . Astérisque , : 159 – 160 .
  • Tits , J. 1974 . Buildings of Spherical Type and Finite BN-Pairs , Lecture Notes in Math. 386 Heidelberg : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.