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On the vanishing of local cohomology modules

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Bibliography

  1. Barth, W.:Transplanting cohomology classes in complex-projective space. Am. J. Math.92, 951–967 (1970).

    Google Scholar 

  2. Bollobás, B.:Graph Theory. Springer: Berlin, Heidelberg, New York: Graduate Texts in Math.,63, 1979

    Google Scholar 

  3. Brodmann, M., Rung, J.:Local cohomology and the connectedness dimension in algebraic varieties. Comment. Math. Helv.61, 481–490 (1986)

    Google Scholar 

  4. Bruns, W., Vetter, U.:Determinantal Rings. (Lect. Notes Math. Vol. 1327) Berlin, Heidelberg, New York: Springer

  5. Chevalley, C.:Some Properties of Ideals in Rings of Power Series. Trans. Am. Math. Soc.,55, 68–84 (1944)

    Google Scholar 

  6. Faltings, G.:Über lokale Kohomologiegruppen hoher Ordnung. J. Reine Angewandte Math.313, 43–51 (1980)

    Google Scholar 

  7. Faltings, G.:Some Theorems about Formal Functions. Publ. Res. Inst. Math. Sci. Kyoto Univ.16, 721–737 (1980)

    Google Scholar 

  8. Fulton, W., Hansen, J.:A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings. Ann. Math.,109, 159–166 (1979)

    Google Scholar 

  9. Fulton, W., Lazersfeld, R.:Connectivity and its applications in Algebraic Geometry, Springer: Berlin, Heidelberg, New York, Lecture Notes in Math.,862, 26–92 (1980)

    Google Scholar 

  10. Gilmer, R.:Integral Dependence in Power Series Rings. J. Algebra,11, 488–502 (1969)

    Google Scholar 

  11. Grothendieck, A.:Local Cohomology (Lect. Notes Math. Vol. 41, Berlin Heidelberg New York: Springer 1966

    Google Scholar 

  12. Grothendieck, A.:E.G.A. IV, Publications Math. I.H.E.S., 28, 32, 000

  13. Hartshorne, R.:Cohomological Dimension of Algebraic Varieties. Ann Math.,88, 403–450 (1968)

    Google Scholar 

  14. Hartshorne, R.:Ample Subvarieties of Algebraic Varieties. (Lect. Notes Math. Vol. 156) Berlin, Heidelberg, New York: Springer 1970

    Google Scholar 

  15. Hartshorne, R.:Algebraic De Rham cohomology. Manu. Math.,7, 125–140 (1972)

    Google Scholar 

  16. Hartshorne, R., Speiser, R.:Local cohomological dimension in characteristic p. Ann. Math.,105, 45–79 (1977)

    Google Scholar 

  17. Jacobson, N.:Abstract Algebra. Vol. 3, Van Nostrand, New York 1964

    Google Scholar 

  18. Lyubeznik, G.:Some Algebraic Sets of High Local Cohomological Dimension in Projective Space. Proc. Am. Math. Soc.95, pp. 9–10 (1985)

    Google Scholar 

  19. Lyubeznik, G.: Etale cohomological dimension and the topology of algebraic varieties (to appear)

  20. Matsumura, H.:Commutative Algebra. Benjamin, New York 1970

    Google Scholar 

  21. Ogus, A.:Local Cohomological Dimension of Algebraic Varieties. Ann. Math.,98, 327–365 (1973)

    Google Scholar 

  22. Peskine, C., Szpiro, L.:Dimension Projective Finie et Cohomologie Locale. I.H.E.S.,42, 323–395 (1973)

    Google Scholar 

  23. Peternell, M.: ein Lefschetz-Satz für schnitte in projektiv algebraischen Mannigfaltigkeiten. Math. Annalen264, 361–388 (1983)

    Google Scholar 

  24. Ratliff, L.J.:Chain Conjectures in Ring Theory. (Lect. Notes Math. Vol. 647) Berlin, Heidelberg, New York: Springer 1978

    Google Scholar 

  25. Rotman, J.:An Introduction to Homological Algebra, New York: Academic Press, 1979

    Google Scholar 

  26. Serre, J.P.:Algebre Locale Multiplicities (Lect. Notes Math. Vol. 11), Berlin, Heidelberg, New York: Springer 1965

    Google Scholar 

  27. Spanier, E.H.:Algebraic Topology. Springer: Berlin, Heidelberg, New York, 1966

    Google Scholar 

  28. Speisen, R.: Cohomological dimension of non-complete hypersurfaces. Invent. Math.21, 143–150 (1973)

    Google Scholar 

  29. Vasoncelos, W.:Ideals generated by R-sequences. J. Algebra,6, pp. 309–316 (1967)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, Indiana, USA

    C. Huneke

  2. Department of Mathematics, University of Chicago, 60637, Chicago, Illinois, USA

    G. Lyubeznik

Authors
  1. C. Huneke
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  2. G. Lyubeznik
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Oblatum 17-XII-1988 & 27-XI-1989

Both authors were partially supported by NSF

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Huneke, C., Lyubeznik, G. On the vanishing of local cohomology modules. Invent Math 102, 73–93 (1990). https://doi.org/10.1007/BF01233420

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