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The transversality of a general translate. (English) Zbl 0288.14014


MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14N10 Enumerative problems (combinatorial problems) in algebraic geometry
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References:

[1] M. Golubitsky and V. Guillemin : Stable mappings and their singularities . Graduate texts in Mathematicas 14 Springer-Verlag (1973). · Zbl 0294.58004
[2] A. Grothendieck and J. Dieudonné : Eléments de géométrie algébrique . Chapitre IV, 2eme, 3eme, 4e parties, Publ. Math. No. 24, 28, 32 IHES (1965, 1966, 1967) (cited EGA IV2, EGA IV3, EGA IV4). | · Zbl 0203.23301
[3] M. Hochster : Grassmannians and their Schubert subvarieties are arithmetically Cohen-Macaulay . J. Algebra 25 (1973) 40-57. · Zbl 0256.14024
[4] W.V.D. Hodge and D. Pedoe : Methods of algebraic geometry . Volume II, Cambridge University Press (1952). · Zbl 0048.14502
[5] G. Kempf : Schubert methods with an application to algebraic curves . Lecture notes, Mathematisch Centrum Amsterdam (1971). · Zbl 0223.14018
[6] S. Kleiman : Geometry on grassmannians and applications to splitting bundles and smoothing cycles, in the ’Zariski volume’ . Publ. Math. IHES 36 (1969) 281-297. · Zbl 0208.48501
[7] D. Laksov : The arithmetic Cohen Macaulay character of Schubert schemes . Acta Math. 129 (1972) 1-9. · Zbl 0233.14012
[8] C. Musili : Postulation formula for Schubert varieties . J. Indian Math. Soc. 36 (1972) 143-171. · Zbl 0277.14021
[9] T. Svanes : Coherent cohomology on Schubert subschemes of flag schemes and applications . (to appear). · Zbl 0308.14008
[10] O. Zariski : The theorem of Bertini on the variable singular points of a linear system of varieties . TAMS, Vol. 56, No. 1, pp. 130-140, July 1944. · Zbl 0061.33101
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