Skip to main content
Log in

Characteristic varieties and vanishing cycles

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  • [AnLe] Angéniol, B., Lejeune-Jalabert, M.: Le théorème de Riemann-Roch singulier pour lesD-modules. Orsay 1984 (Preprint)

  • [BV] Barbasch, D., Vogan, D.: Primitive ideals and orbital integrals in complex groups I, II. Math. Ann.259, 153–199 (1982); J. Algebra80, 350–382 (1983)

    Google Scholar 

  • [Beil] Beilinson, A.: On the derived category of holonomic modules. Moscow 1985 (Preprint)

  • [BeBe] Beilinson, A., Bernstein, J.: Localization de\(\mathfrak{g}\)-modules. C.R. Acad. Sc. Paris292, 15–18 (1981)

    Google Scholar 

  • [Be 1] Bernstein, I.N.: Modules over a ring of differential operators. Funct. Anal. Appl.5, 98–101 (1971)

    Google Scholar 

  • [Be 2] Bernstein, J.: Algebraic theory ofD-modules. 1982 (Preprint)

  • [BBD] Beilinson, A., Bernstein, J., Deligne, P.: Faisceaux pervers. Astérisque,100 (1982)

  • [BGG] Bernstein, I.N., Gel'fand, I.M., Gel'fand, S.I.: Category of\(\mathfrak{g}\)-modules Funct. Anal. Appl.10, 1–18 (1976)

    Google Scholar 

  • [BB 1] Borho, W., Brylinski, J.-L.: Differential operators on homogeneous spaces. I. Invent. Math.69, 437–476 (1982)

    Google Scholar 

  • [BB 2] Borho, W., Brylinski, J.-L.: Differential operators on homogeneous spaces III. (Preprint IHES, 1984)

  • [Br 1] Brylinski, J.-L.: (Co-)homologie d'intersection et faisceaux pervers. Séminaire Bourbaki no 585, février 1982

  • [Br 2] Brylinski, J.-L.: Transformations canoniques et transformation de Fourier (prépublication 1982)

  • [BDK] Brylinski, J.-L., Dubson, A., Kashiwara, M.: Formule de l'indice pour les modules holonômes et obstruction d'Euler locale. C.R. Acad. Sc. Paris (26-10-1981)

  • [BK] Brylinski, J.-L., Kashiwara, M.: Kazhdan-Lusztig conjecture and holonomic systems. Invent. Math.64, 387–410 (1981)

    Google Scholar 

  • [BMV] Brylinski, J.-L., Malgrange, B., Verdier, J.-L.: C.R. Acad. Sc. Paris.297, 55–58 (4 juillet 1983)

    Google Scholar 

  • [D 1] Deligne, P.: SGA 7 exposé XIV Lecture Notes 340

  • [D 2] Deligne, P.: Lettre à MacPherson, march 1982

  • [Du 1] Dubson, A.: Calcul des invariants numériques des singularités et applications (Prépublication, S.t.B. Theor. Math. Universität Bonn. 1981)

  • [Du 2] Dubson, A.: Classes caractéristiques des variétés singulières. C.R. Acad. Sc. Paris,287, 237–240 (11–1978)

    Google Scholar 

  • [Du 3] Dubson, A.: C.R. Acad. Sc. Paris.299, 113–116 (1984);299, 6, 181–184 (1984)

    Google Scholar 

  • [FM 1] Fulton, W., MacPherson, R.: Intersecting cycles on an algebraic variety. Proc. Nordic Summer School, p. 179–197. Oslo, 1976

  • [FM 2] Fulton, W., MacPherson, R.: Categorical framework for the study of singular spaces. Memoirs Am. Math. Soc.31, 243 (1981)

    Google Scholar 

  • [Ga] Gabber, O.: The integrability of the characteristic variety. Am. J. Math.103, 445–468 (1981)

    Google Scholar 

  • [Gi 1] Ginsburg, V.: Symplectic geometry and representations. J. Funct. Anal. Appl.17, 75–76 (1983)

    Google Scholar 

  • [Gi 2] Ginsburg, V.:\(\mathfrak{g}\)-modules, Springer's representations and bivariant Chern classes. Moscow 1984 (Preprint)

  • [Gi 3] Ginsburg, V.: Lagrangian construction for representations of Hecke algebras. Moscow 1984 (Preprint)

  • [Gon] Gonzalez-Sprinberg, G.: L'obstruction locale d'Euler et le théorème de MacPherson. Astérisque8–82, 7–32 (1981)

    Google Scholar 

  • [H] Hotta, R.: On Joseph's construction of Weyl group representations. Tohoku Math. J.36, 49–74 (1984)

    Google Scholar 

  • [J 1] Joseph, A.: Goldie rank in the enveloping algebra of a semi-simple Lie algebra I, II. J. Algebra65, 269–306 (1980)

    Google Scholar 

  • [J 2] Joseph, A.: On the variety of a highest weight module. Paris 1982 (Preprint)

  • [J 3] Joseph, A.: On the associated variety of a primitive ideal. Paris 1983 (Preprint)

  • [K 1] Kashiwara, M.: Proc. Jap. Acad.,49, 803–804 (1973)

    Google Scholar 

  • [K 2] Kashiwara, M.:B-function and holonomic systems. Invent. Math.38, 33–53 (1976)

    Google Scholar 

  • [K 3] Kashiwara, M.: On holonomic systems of differential equations II. Invent. Math.49, 121–135 (1978)

    Google Scholar 

  • [K 4] Kashiwara, M.: Systèmes d'équations micro-différentielles. Redigé par T. Fernandes. Boston, Basel, Stuttgart: Birkhäuser. Prog. Math.34 (1983)

    Google Scholar 

  • [K 5] Kashiwara, M.: Vanishing cycles for holonomic systems. Lect. Notes. Math.1016, 134–142 (1983)

    Google Scholar 

  • [K 6] Kashiwara, M.: The Riemann-Hilbert problem for holonomic systems. Publ. Res. Inst. Math. Sci.20, 319–365 (1984)

    Google Scholar 

  • [K 7] Kashiwara, M.: The characteristic cycle and the index formula for constructible sheaves. (Preprint Res. Inst. Math. Sci. 1983)

  • [KK 1] Kashiwara, M., Kawai, T.: On the Characteristic variety of a holonomic system with regular singularities. Adv. Math.34, 163–184 (1979)

    Google Scholar 

  • [KK 2] Kashiwara, M., Kawai, T.: On holonomic systems of linear differential equations III (systems with regular singularities). Publ. Res. Inst. Math. Sci.17, 813–979 (1981)

    Google Scholar 

  • [KK 3] Kashiwara, M., Kawai, T.: Second-microlocalization and asymptotic expansions. Lect. Notes Phys.126, 21–76 (1980)

    Google Scholar 

  • [KS 1] Kashiwara, M., Shapira, P.: Problème de Cauchy pour les systèmes micro-différentiels. Invent. Math.46, 17–38 (1978)

    Google Scholar 

  • [KS 2] Kashiwara, M., Shapira, P.: Micro-hyperbolic systems. Acta Math.142, 1–55 (1979)

    Google Scholar 

  • [KS 3] Kashiwara, M., Shapira, P.: Variété charactéristique de la restriction d'un module différentiel. (Prépublication de l'Ecole Polytéchnique, 1981)

  • [KS 4] Kashiwara, M., Shapira, P.: Micro-support d'un faisceau. Note à C.R. Acad. Sc. Paris,295, 487–491 (1982)

    Google Scholar 

  • [KS 5] Kashiwara, M., Shapira, P.: Microlocal study of sheaves. (Preprint Res. Inst. Math. Sci. 1984)

  • [KT] Kashiwara, M., Tanisaki, T.: The characteristic cycles of holonomic systems on a flag manifold. Invent. Math.77, 185–198 (1984)

    Google Scholar 

  • [KL] Kazhdan, D., Lusztig, G.: A topological approach to Springer's representations. Adv. Math.38, 222–228 (1980)

    Google Scholar 

  • [La 1] Laumon, G.: Sur la catégorie dériveé desD-modules filtrés. Thèse d'Etat, Orsay 1983

  • [La 2] Laumon, G.: Transformations canoniques et spécialisation pour lesD-modules filtrés. (à paraitre dans Astérisque)

  • [Lev] Levasseur. Exposé of a lecture of O. Gabber. Paris 1982

  • [Le] Le Dung Trang. (To appear)

  • [LeMe] Le Dung Trang, Mebkhout, Z.: Variétés caractéristiques et variétés polaires. C.R. Acad. Sc. Paris.296, 129–132 (1983)

    Google Scholar 

  • [Mac] MacPherson R.: Chern classes for singular varieties. Ann. Math.100, 423–432 (1974)

    Google Scholar 

  • [MacV] MacPherson, R., Vilonen, K.: Construction élémentaires des faisceaux pervers. C.R. Acad. Sc. Paris.299, 10, 443–446 (1984)

    Google Scholar 

  • [Ma 1] Malgrange, B.: Polynômes de Bernstein-Sato et cohomologie évanescente. Astérisque101–102, 243–267 (1983)

    Google Scholar 

  • [Ma 2] Malgrange, B.: Rapport sur les théorèmes d'indice de Boutet de Monvel à Kashiwara. Astérisque101–102, 230–242 (1982)

    Google Scholar 

  • [Ma 3] Malgrange, B.: Sur les images directes deD-modules. (Preprint 1984)

  • [Me 1] Mebkhout, Z.: Ark. Math.20, 111–124 (1982)

    Google Scholar 

  • [Me 2] Mebkhout, Z.: Une équivalence de catégories. Comput. Math.51, 51–62 (1984); Une autre équivalence de catégories. ibid. 63–88

    Google Scholar 

  • [Sab] Sabbah, C.: Quelques remarques sur la géométrie des espaces conormaux. (à paraître dans Astérisque)

  • [SKK 1] Sato, M., Kawai, T., Kashiwara, M.: Hyper-functions and pseudodifferential equations. Lect. Notes Math.287 (1972)

  • [SKK 2] Sato, M., Kawai, T., Kashiwara, M.: Micro-local Analysis of Prehomogeneous vector spaces. Invent. Math.62, 117–179 (1980)

    Google Scholar 

  • [Ver 1] Verdier, J.-L.: Seminaire de géométrie analytique, exp. IX. Astérisque 36–37

  • [Ver 2] Verdier, J.-L.: Spécialisation de faisceaux et monodromic modérée. Astérisque101–102, 332–364 (1983)

    Google Scholar 

  • [Ver 3] Verdier, J.-L.: Géométrie microlocale. Lect. Notes Math.1016, 117–133 (1983)

    Google Scholar 

  • [Ver 4] Verdier, J.-L.: Prolongement des faisceaux pervers monodromiques. (à paraître dans Astérisque)

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ginsburg, V. Characteristic varieties and vanishing cycles. Invent Math 84, 327–402 (1986). https://doi.org/10.1007/BF01388811

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388811

Keywords

Navigation