# Zeros of holomorphic vector fields on singular spaces and intersection rings of Schubert varieties

E. Akyildiz; J. B. Carrell; D. I. Lieberman

Compositio Mathematica (1986)

- Volume: 57, Issue: 2, page 237-248
- ISSN: 0010-437X

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topAkyildiz, E., Carrell, J. B., and Lieberman, D. I.. "Zeros of holomorphic vector fields on singular spaces and intersection rings of Schubert varieties." Compositio Mathematica 57.2 (1986): 237-248. <http://eudml.org/doc/89755>.

@article{Akyildiz1986,

author = {Akyildiz, E., Carrell, J. B., Lieberman, D. I.},

journal = {Compositio Mathematica},

keywords = {toric action; cohomology rings of invariant subvarieties; holomorphic vector field; cohomology algebra of a Schubert variety},

language = {eng},

number = {2},

pages = {237-248},

publisher = {Martinus Nijhoff Publishers},

title = {Zeros of holomorphic vector fields on singular spaces and intersection rings of Schubert varieties},

url = {http://eudml.org/doc/89755},

volume = {57},

year = {1986},

}

TY - JOUR

AU - Akyildiz, E.

AU - Carrell, J. B.

AU - Lieberman, D. I.

TI - Zeros of holomorphic vector fields on singular spaces and intersection rings of Schubert varieties

JO - Compositio Mathematica

PY - 1986

PB - Martinus Nijhoff Publishers

VL - 57

IS - 2

SP - 237

EP - 248

LA - eng

KW - toric action; cohomology rings of invariant subvarieties; holomorphic vector field; cohomology algebra of a Schubert variety

UR - http://eudml.org/doc/89755

ER -

## References

top- [A] E. Akyildiz: Vector fields and cohomology of G/P, Lecture Notes in Math., Vol. 956 (1981). Zbl0498.14025MR704982
- [ACLS1] E. Akyildiz, J.B. Carrell, D.I. Lieberman and A.J. Sommese: Graded rings associated to holomorphic vector fields with a unique zero. Proc. of Symp. in Pure Mathematics: Singularities, Vol. 40 (1983) 55. Zbl0523.57031MR713045
- [ACLS 2] E. Akyildiz, J.B. Carrell, D.I. Lieberman and A.J. Sommese: Graded rings associated to holomorphic vector fields with a unique zero. Preprint. Zbl0523.57031
- [BGG] I.N. Bernstein, I.M. Gel'fand and S.I. Gel'fand: Schubert cells and cohomology of the space G/P, Russian Math. Surveys28 (1973) 1-26. Zbl0289.57024MR429933
- [C 1] J.B. Carrell: Vector fields and the cohomology of G/B. Manifolds and Lie groups, Papers in honor of Y. Matsushima. Progress in Mathematics, Vol. 14Birkhauser, Boston (1981). Zbl0482.57017MR642851
- [C 2] J.B. Carrell: Orbits of the Weyl group and a theorem of DeConcini and Procesi. Preprint. Zbl0613.20029
- [CL1] J.B. Carrell and D.I. Lieberman: Holomorphic vector fields and compact Kaehler manifolds, Inventiones Math.21 (1973) 303-309. Zbl0253.32017MR326010
- [CL2] J.B. Carrell and D.I. Lieberman: Vector fields and Chern numbers, Math. Annalen, 225 (1977) 263-273. Zbl0365.32020MR435456
- [CL3] J.B. Carrell and D.I. Lieberman: Vector fields, Chern classes and cohomology, Proc. Symp. Pure Math., Vol. 30 (1977) 251-254. Zbl0365.32019MR460734
- [CS] J.B. Carrell and A.J. Sommese, Some topological aspects of C*-actions on compact Kaehler manifolds, Comment. Math. Helv.54 (1979) 567-582. Zbl0466.32015MR552677
- [DP] C. Deconcini and C. Procesi: Symmetric functions, conjugacy classes, and the flag variety, Invent. Math., 64 (1981) 203-219. Zbl0475.14041MR629470
- [D] P. Deligne: Théorie de Hodge, III. Inst. Hautes Etudes Sci. Publ. Math., Vol. 44 (1972) 5-77. Zbl0237.14003MR498552
- [F] A. Fujiki: Fixed points of the actions on compact Kaehler manifolds, Publ. RIMS, Kyoto Univ.15 (1979) 1-45. Zbl0446.53021MR566083
- [GH] P. Griffiths and J. Harris: Principles of Algebraic Geometry, John Wiley and Sons, New York (1978). Zbl0408.14001MR507725
- [H] H. Hironaka: Bimeromorphic smoothing of a complex analytic space, Math. Inst. Warwick Univ., England (1971). Zbl0407.32006
- [Ku1] S. Kumar: Geometry of Schubert cells and cohomology of Kac-Moody Lie algebras, J. of Diff. Geometry20 (1984) 389-432. MR788286
- [Ku 2] S. Kumar: Cohomology algebra of Schubert varieties associated to Kac-Moody groups, to appear in proceedings of the CMS Seminar in Algebraic Geometry, Vancouver (1984). Zbl0591.14037MR846024

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