On the syzygies of flag manifolds
HTML articles powered by AMS MathViewer
- by Laurent Manivel PDF
- Proc. Amer. Math. Soc. 124 (1996), 2293-2299 Request permission
Abstract:
We show that on a complex flag manifold, a very ample line bundle which is a $p$-th power has property $N_p$ in the sense of Green and Lazarsfeld. This is a partial answer to a problem raised by Fulton.References
- Kaan Akin, David A. Buchsbaum, and Jerzy Weyman, Schur functors and Schur complexes, Adv. in Math. 44 (1982), no. 3, 207–278. MR 658729, DOI 10.1016/0001-8708(82)90039-1
- Aaron Bertram, Lawrence Ein, and Robert Lazarsfeld, Vanishing theorems, a theorem of Severi, and the equations defining projective varieties, J. Amer. Math. Soc. 4 (1991), no. 3, 587–602. MR 1092845, DOI 10.1090/S0894-0347-1991-1092845-5
- Michel Demazure, A very simple proof of Bott’s theorem, Invent. Math. 33 (1976), no. 3, 271–272. MR 414569, DOI 10.1007/BF01404206
- Lawrence Ein and Robert Lazarsfeld, Syzygies and Koszul cohomology of smooth projective varieties of arbitrary dimension, Invent. Math. 111 (1993), no. 1, 51–67. MR 1193597, DOI 10.1007/BF01231279
- Mark L. Green, Koszul cohomology and the geometry of projective varieties, J. Differential Geom. 19 (1984), no. 1, 125–171. MR 739785
- G. Kempf, The projective coordinate ring of abelian varieties, Algebraic Analysis, Geometry and Number Theory (J. I. Igusa, ed.), Johns Hopkins Press, Baltimore, 1989.
- Alain Lascoux, Syzygies des variétés déterminantales, Adv. in Math. 30 (1978), no. 3, 202–237 (French). MR 520233, DOI 10.1016/0001-8708(78)90037-3
- I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
- P. Pragacz and J. Weyman, Ideals generated by Pfaffians, J. Algebra 61 (1979), 189–198.
- T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
Additional Information
- Laurent Manivel
- Affiliation: Institut Fourier, Université de Grenoble I, 38402 Saint Martin d’Hères, France
- MR Author ID: 291751
- ORCID: 0000-0001-6235-454X
- Email: laurent.manivel@ujf-grenoble.fr
- Received by editor(s): November 28, 1994
- Communicated by: Eric M. Friedlander
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 2293-2299
- MSC (1991): Primary 14M15; Secondary 13D02, 14F17
- DOI: https://doi.org/10.1090/S0002-9939-96-03775-6
- MathSciNet review: 1372039