The arithmetic Cohen-Macaulay character of Schubert schemes. (English) Zbl 0233.14012


14M15 Grassmannians, Schubert varieties, flag manifolds
13C10 Projective and free modules and ideals in commutative rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Full Text: DOI


[1] Altman, A., & Kleiman, S. L.,Introduction to Grothendieck duality theory. Lecture notes in mathematics no. 146, Springer Verlag, 1970. · Zbl 0215.37201
[2] Bourbaki, N.,Algèbre, Chap. 3. Algèbre Multilinéaire. Act. Sci. Ind. 1044, Hermann, 1948. · Zbl 0039.25902
[3] Eagon, J. A., &Hochster, M., A class of perfect determinental ideals.Bull. Amer. Math. Soc. 76 (1970), 1026–1029. · Zbl 0201.37201 · doi:10.1090/S0002-9904-1970-12543-5
[4] Grothendieck, A. (with J. Dieudonné), Eleménts de géométrie algébrique. Chap. III.Publ. Math. I.H.E.S., 17 (1963) and Chap. IV,ibid. Publ. Math. I.H.E.S., 24 (1965).
[5] Hochster, M., Cohen-Macaulay rings of invariants, rings generated by monomials, and polytypes. Notices Amer. Math. Soc., 18 (1971), 509.
[6] Hodge, W. V. D. & Pedoe, D.,Methods of algebraic geometry, vol. I and II. Cambridge Univ. Press, 1968. · Zbl 0157.27501
[7] Igusa, J.-I., On the arithmetic normality of the Grassmann variety.Proc. Nat. Acad. Sci. U.S.A., 40 (1954), 309–313. · Zbl 0055.39002 · doi:10.1073/pnas.40.5.309
[8] Kleiman, S. L., Geometry of Grassmannians and applications to splitting bundles and smoothing cycles.Publ. Math. I.H.E.S., 36 (1969), 281–298. · Zbl 0208.48501
[9] Kleiman, S. L., & Landolfi, J., Geometry and deformations of special Schubert varieties. (To appear inCompositio. Math.) · Zbl 0238.14007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.