Duke Mathematical Journal

Flags, Schubert polynomials, degeneracy loci, and determinantal formulas

William Fulton

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Article information

Source
Duke Math. J. Volume 65, Number 3 (1992), 381-420.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077295265

Mathematical Reviews number (MathSciNet)
MR1154177

Zentralblatt MATH identifier
0788.14044

Digital Object Identifier
doi:10.1215/S0012-7094-92-06516-1

Subjects
Primary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15]
Secondary: 14M12: Determinantal varieties [See also 13C40] 14M15: Grassmannians, Schubert varieties, flag manifolds [See also 32M10, 51M35]

Citation

Fulton, William. Flags, Schubert polynomials, degeneracy loci, and determinantal formulas. Duke Math. J. 65 (1992), no. 3, 381--420. doi:10.1215/S0012-7094-92-06516-1. http://projecteuclid.org/euclid.dmj/1077295265.


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References

  • [BGG] I. N. Bernšteĭ n, I. M. Gel'fand, and S. I. Gel'fand, Schubert cells, and the cohomology of the spaces $G/P$, Uspehi Mat. Nauk 28 (1973), no. 3(171), 3–26.
  • [BS] R. Bott and H. Samelson, Applications of the theory of Morse to symmetric spaces, Amer. J. Math. 80 (1958), 964–1029.
  • [BFL] P. Bressler, M. Finkelberg, and V. Lunts, Vanishing cycles on Grassmannians, Duke Math. J. 61 (1990), no. 3, 763–777.
  • [C1], Séminaire C. Chevalley, 1956–1958. Classification des groupes de Lie algébriques, 2 vols, Secrétariat mathématique, 11 rue Pierre Curie, Paris, 1958.
  • [C2] C. Chevalley, Séminaire C. Chevalley; 2e année: 1958. Anneaux de Chow et applications, Secrétariat mathématique, 11 rue Pierre Curie, Paris, 1958.
  • [D] M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53–88.
  • [E] C. Ehresmann, Sur la topologie de certains espaces homogènes, Ann. of Math. (2) 35 (1934), 396–443.
  • [F] W. Fulton, Intersection theory, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 2, Springer-Verlag, Berlin, 1984.
  • [G1] G. Giambelli, Ordine de una varietà piu ampia di quella rappresentata coll' annullare tutti i minori di dato ordine estratti da una data matrice generica di forme, Mem. R. Istituto Lombardo (3) 11 (1904), 101–125.
  • [G2] G. Giambelli, La teoria delle formole d'incidenza e di posizione speciale e le forme binarie, Atti della R. Accad. delle Scienze di Torino 40 (1904), 1041–1062.
  • [G3] G. Giambelli, Risoluzione del problema generale numerativo per gli spazi plurisecanti di una curva algebrica, Mem. Acad. Sci. Torino (2) 59 (1909), 433–508.
  • [K] G. Kempf, Linear systems on homogeneous spaces, Ann. of Math. (2) 103 (1976), no. 3, 557–591.
  • [KL] G. Kempf and D. Laksov, The determinantal formula of Schubert calculus, Acta Math. 132 (1974), 153–162.
  • [L1] A. Lascoux, Puissances extérieures, déterminants et cycles de Schubert, Bull. Soc. Math. France 102 (1974), 161–179.
  • [L2] A. Lascoux, Classes de Chern des variétés de drapeaux, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), no. 5, 393–398.
  • [L3] A. Lascoux, Anneau de Grothendieck de la variété des drapeaux, preprint, 1988.
  • [LS1] A. Lascoux and M.-P. Schützenberger, Polynômes de Schubert, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), no. 13, 447–450.
  • [LS2] A. Lascoux and M.-P. Schützenberger, Symmetry and flag manifolds, Invariant theory (Montecatini, 1982) ed. F. Gherardelli, Lecture Notes in Math., vol. 996, Springer, Berlin, 1983, pp. 118–144.
  • [LS3] A. Lascoux and M.-P. Schützenberger, Schubert polynomials and the Littlewood-Richardson rule, Lett. Math. Phys. 10 (1985), no. 2-3, 111–124.
  • [M] I. G. Macdonald, Notes on Schubert Polynomials, Départment de mathématiques et d'informatique, Université du Québec, Montréal, 1991.
  • [Mo] D. Monk, The geometry of flag manifolds, Proc. London Math. Soc. (3) 9 (1959), 253–286.
  • [MS] C. Musili and C. S. Seshadri, Schubert varieties and the variety of complexes, Arithmetic and geometry, Vol. II, Progr. Math., vol. 36, Birkhäuser Boston, Boston, MA, 1983, Papers Dedicated to I. R. Shafarevich on the Occasion of his Sixtieth Birthday, pp. 329–359.
  • [P] P. Pragacz, Enumerative geometry of degeneracy loci, Ann. Sci. École Norm. Sup. (4) 21 (1988), no. 3, 413–454.
  • [R] A. Ramanathan, Schubert varieties are arithmetically Cohen-Macaulay, Invent. Math. 80 (1985), no. 2, 283–294.
  • [S] T. A. Springer, Quelques applications de la cohomologie d'intersection, Bourbaki Seminar, Vol. 1981/1982, Astérisque, vol. 92, Soc. Math. France, Paris, 1982, pp. 249–273.
  • [W] M. L. Wachs, Flagged Schur functions, Schubert polynomials, and symmetrizing operators, J. Combin. Theory Ser. A 40 (1985), no. 2, 276–289.