Line bundles on Bott-Samelson varieties
Authors:
Niels Lauritzen and Jesper Funch Thomsen
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).
BS R. Bott and H. Samelson, Application of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964–1029.
Dem M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. Ec. Norm. Sup. 7 (1974), 53–88.
HanMS H. C. Hansen, On cycles on flag manifolds, Math. Scand. 33 (1973), 269–274.
HanSpec H. C. Hansen Cykler på flagmangfoldigheder, speciale, Aarhus Universitet (1972).
Kumar S. Kumar, Demazure character formula in arbitrary Kac-Moody setting, Invent. Math. 89 (1987), 395–423.
LLM V. Lakshmibai, P. Littelmann and P. Magyar, Standard monomial theory for Bott-Samelson varieties, Compos. Math. 130 (2002), 293–318.
MR V. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Annals of Math. 122 (1985), 27–40.
Ram A. Ramanathan, Schubert varieties are arithmetically Cohen Macaulay, Invent. Math. 80 (1985), 283–294.
BS R. Bott and H. Samelson, Application of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964–1029.
Dem M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. Ec. Norm. Sup. 7 (1974), 53–88.
HanMS H. C. Hansen, On cycles on flag manifolds, Math. Scand. 33 (1973), 269–274.
HanSpec H. C. Hansen Cykler på flagmangfoldigheder, speciale, Aarhus Universitet (1972).
Kumar S. Kumar, Demazure character formula in arbitrary Kac-Moody setting, Invent. Math. 89 (1987), 395–423.
LLM V. Lakshmibai, P. Littelmann and P. Magyar, Standard monomial theory for Bott-Samelson varieties, Compos. Math. 130 (2002), 293–318.
MR V. Mehta and A. Ramanathan, Frobenius splitting and cohomology vanishing for Schubert varieties, Annals of Math. 122 (1985), 27–40.
Ram 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
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
