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Line bundles on Bott-Samelson varieties
Author(s):
Niels
Lauritzen;
Jesper
Funch
Thomsen
Journal:
J. Algebraic Geom.
13
(2004),
461-473.
Posted:
December 8, 2003
MathSciNet review:
2047677
Retrieve article in:
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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:
-
- 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:
10.1090/S1056-3911-03-00358-8
PII:
S 1056-3911(03)00358-8
Received by editor(s):
January 22, 2002
Posted:
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
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