On the ampleness of homogeneous vector bundles

Snow, Dennis M.

doi:10.1090/S0002-9947-1986-0825723-9

On the ampleness of homogeneous vector bundles

Author: Dennis M. Snow
Journal: Trans. Amer. Math. Soc. 294 (1986), 585-594
MSC: Primary 32M10; Secondary 14M17, 32L15
DOI: https://doi.org/10.1090/S0002-9947-1986-0825723-9
MathSciNet review: 825723
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A formula is proved which expresses the ampleness of a homogeneous vector bundle over $G/P$ in terms of the distance of the weights of the representation of $P$ to certain dominant weights of $G$.

Armand Borel, Linear algebraic groups, W. A. Benjamin, Inc., New York-Amsterdam, 1969. Notes taken by Hyman Bass. MR 0251042
Raoul Bott, Homogeneous vector bundles, Ann. of Math. (2) 66 (1957), 203–248. MR 89473, DOI https://doi.org/10.2307/1969996
Roger W. Carter, Simple groups of Lie type, John Wiley & Sons, London-New York-Sydney, 1972. Pure and Applied Mathematics, Vol. 28. MR 0407163
Edward Cline, Brian Parshall, and Leonard Scott, Induced modules and affine quotients, Math. Ann. 230 (1977), no. 1, 1–14. MR 470094, DOI https://doi.org/10.1007/BF01420572
Norman Goldstein, Ampleness and connectedness in complex $G/P$, Trans. Amer. Math. Soc. 274 (1982), no. 1, 361–373. MR 670938, DOI https://doi.org/10.1090/S0002-9947-1982-0670938-2
Robin Hartshorne, Ample vector bundles, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 63–94. MR 193092
James E. Humphreys, Linear algebraic groups, Springer-Verlag, New York-Heidelberg, 1975. Graduate Texts in Mathematics, No. 21. MR 0396773

J.-P. Serre, Représentations linéaires et espaces homogènes Kählerians des groupes de Lie compacts (d’après Borel et Weil), Sém. Bourbaki, Exposé 100, May 1954, Benjamin, New York, 1966.

Andrew John Sommese, Submanifolds of Abelian varieties, Math. Ann. 233 (1978), no. 3, 229–256. MR 466647, DOI https://doi.org/10.1007/BF01405353
Andrew John Sommese, A convexity theorem, Singularities, Part 2 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 497–505. MR 713275
Robert Steinberg, On the desingularization of the unipotent variety, Invent. Math. 36 (1976), 209–224. MR 430094, DOI https://doi.org/10.1007/BF01390010