Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Line bundles on Bott-Samelson varieties


Authors: Niels Lauritzen and Jesper Funch Thomsen
Translated by:
Journal: J. Algebraic Geom. 13 (2004), 461-473
DOI: https://doi.org/10.1090/S1056-3911-03-00358-8
Published electronically: December 8, 2003
MathSciNet review: 2047677
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Abstract | References | Additional Information

Abstract: We characterize the globally generated, ample and very ample line bundles on Bott-Samelson varieties. Using Frobenius splitting we prove a vanishing theorem generalizing the vanishing theorem of Kumar in characteristic zero (Invent. Math. 89 (1987), 395-423).


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

  • 1. R. Bott and H. Samelson, Application of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964-1029.
  • 2. M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. Ec. Norm. Sup. 7 (1974), 53-88.
  • 3. H. C. Hansen, On cycles on flag manifolds, Math. Scand. 33 (1973), 269-274.
  • 4. H. C. Hansen Cykler påflagmangfoldigheder, speciale, Aarhus Universitet (1972).
  • 5. S. Kumar, Demazure character formula in arbitrary Kac-Moody setting, Invent. Math. 89 (1987), 395-423.
  • 6. V. Lakshmibai, P. Littelmann and P. Magyar, Standard monomial theory for Bott-Samelson varieties, Compos. Math. 130 (2002), 293-318.
  • 7. V. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Annals of Math. 122 (1985), 27-40.
  • 8. A. Ramanathan, Schubert varieties are arithmetically Cohen Macaulay, Invent. Math. 80 (1985), 283-294.


Additional Information

Niels Lauritzen
Affiliation: Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, DK-8000 Århus C, Denmark
Email: niels@imf.au.dk

Jesper Funch Thomsen
Affiliation: Institut for Matematiske Fag, Aarhus Universitet, Ny Munkegade, DK-8000 Århus C, Denmark.
Email: funch@imf.au.dk

DOI: https://doi.org/10.1090/S1056-3911-03-00358-8
Received by editor(s): January 22, 2002
Published electronically: December 8, 2003
Additional Notes: Both authors were supported in part by the TMR-programme “Algebraic Lie Representations” (ECM Network Contract No. ERB FMRX-CT 97/0100) and the Danish Natural Science Research Council

American Mathematical Society