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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
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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

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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