Numerical invariants of perverse sheaves
David B. Massey
Source: Duke Math. J. Volume 73, Number 2
(1994), 307-369.
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References
[BBD] A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces I (Luminy, 1981), Astérisque, vol. 100, Soc. Math. France, Paris, 1982, pp. 5–171.
Mathematical Reviews (MathSciNet): MR86g:32015
Zentralblatt MATH: 0536.14011
[Br] J. Brylinski, Transformations canoniques, dualité projective, théorie de Lefschetz, transformations de Fourier et sommes trigonométriques, Astérisque (1986), no. 140-141, 3–134, 251.
Mathematical Reviews (MathSciNet): MR88j:32013
Zentralblatt MATH: 0624.32009
[BDK] J. Brylinski, A. Dubson, and M. Kashiwara, Formule de l'indice pour modules holonomes et obstruction d'Euler locale, C. R. Acad. Sci. Paris Sér. I Math. 293 (1981), no. 12, 573–576.
Mathematical Reviews (MathSciNet): MR83a:32010
Zentralblatt MATH: 0492.58021
[C] D. Cohen, Cohomology and intersection cohomology of complex hyperplane arrangements, dissertation, Northeastern Univ., 1992.
Mathematical Reviews (MathSciNet): MR1201844
Zentralblatt MATH: 0787.57014
Digital Object Identifier: doi:10.1006/aima.1993.1007
[Da] J. Damon, Higher multiplicities and almost free divisors and complete intersections, preprint.
Mathematical Reviews (MathSciNet): MR1346928
Zentralblatt MATH: 0867.32015
[De] P. Deligne, Comparaison avec le théorie transcendante, Séminaire de Geometrie Algébrique du Bois-Marie 1967–1969, SGA 7 II, Lecture Notes in Math., vol. 340, Springer-Verlag, Berlin, pp. 116–164.
Zentralblatt MATH: 0266.14009
[Fu] W. Fulton, Intersection Theory, Ergeb. Math. Grenzgeb. (3), vol. 2, Springer-Verlag, Berlin, 1984.
Mathematical Reviews (MathSciNet): MR85k:14004
Zentralblatt MATH: 0541.14005
[Ga] T. Gaffney, Polar multiplicities and equisingularity of map germs, to appear in Topology.
Mathematical Reviews (MathSciNet): MR1204414
Digital Object Identifier: doi:10.1016/0040-9383(93)90045-W
[Gi] V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), no. 2, 327–402.
Mathematical Reviews (MathSciNet): MR87j:32030
Zentralblatt MATH: 0598.32013
Digital Object Identifier: doi:10.1007/BF01388811
[GM1] M. Goresky and R. MacPherson, Morse theory and intersection homology theory, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 135–192.
Mathematical Reviews (MathSciNet): MR86i:32019
Zentralblatt MATH: 0524.57022
[GM2] M. Goresky and R. MacPherson, Stratified Morse Theory, Ergeb. Math. Grenzgeb. (3), vol. 14, Springer-Verlag, Berlin, 1988.
Mathematical Reviews (MathSciNet): MR90d:57039
Zentralblatt MATH: 0639.14012
[GM3] M. Goresky and R. MacPherson, Intersection homology II, Invent. Math. 72 (1983), no. 1, 77–129.
Mathematical Reviews (MathSciNet): MR84i:57012
Zentralblatt MATH: 0529.55007
Digital Object Identifier: doi:10.1007/BF01389130
[GM4] M. Goresky and R. MacPherson, Intersection homology theory, Topology 19 (1980), no. 2, 135–162.
Mathematical Reviews (MathSciNet): MR82b:57010
Zentralblatt MATH: 0448.55004
Digital Object Identifier: doi:10.1016/0040-9383(80)90003-8
[HL] N. Hamm and Lê D. T., Un théorème de Zariski du type de Lefschetz, Ann. Sci. École Norm. Sup. (4) 6 (1973), 317–355.
Mathematical Reviews (MathSciNet): MR53:5582
Zentralblatt MATH: 0276.14003
[Ha] R. Hartshorne, Residues and Duality, Lecture Notes in Math., vol. 20, Springer-Verlag, Berlin, 1966.
Mathematical Reviews (MathSciNet): MR36:5145
Zentralblatt MATH: 0212.26101
[HMS] J. P. Henry, M. Merle, and C. Sabbah, Sur la condition de Thom stricte pour un morphisme analytique complexe, Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 2, 227–268.
Mathematical Reviews (MathSciNet): MR86m:32019
Zentralblatt MATH: 0551.32012
[Hi] H. Hironaka, Normal cones in analytic Whitney stratifications, Inst. Hautes Études Sci. Publ. Math. (1969), no. 36, 127–138.
Mathematical Reviews (MathSciNet): MR43:3492
Zentralblatt MATH: 0219.57022
Digital Object Identifier: doi:10.1007/BF02684601
[I] B. Iversen, Cohomology of Sheaves, Universitext, Springer-Verlag, Berlin, 1986.
Mathematical Reviews (MathSciNet): MR87m:14013
Zentralblatt MATH: 0559.55001
[KS1] M. Kashiwara and P. Schapira, Microlocal study of sheaves, Astérisque (1985), no. 128, 235.
Mathematical Reviews (MathSciNet): MR87f:58159
Zentralblatt MATH: 0589.32019
[KS2] M. Kashiwara and P. Schapira, Sheaves on Manifolds, Grundlehren Math. Wiss., vol. 292, Springer-Verlag, Berlin, 1990.
Mathematical Reviews (MathSciNet): MR92a:58132
Zentralblatt MATH: 0709.18001
[Kl] S. Kleiman, The transversality of a general translate, Compositio Math. 28 (1974), 287–297.
Mathematical Reviews (MathSciNet): MR50:13063
Zentralblatt MATH: 0288.14014
[Lê1] D. T. Lê, Calcul du nombre de cycles évanouissants d'une hypersurface complexe, Ann. Inst. Fourier (Grenoble) 23 (1973), no. 4, 261–270.
Mathematical Reviews (MathSciNet): MR48:8838
Zentralblatt MATH: 0293.32013
[Lê2] D. T. Lê, Le concept de singularité isolée de fonction analytique, Complex analytic singularities, Adv. Stud. Pure Math., vol. 8, North-Holland, Amsterdam, 1987, pp. 215–227.
Mathematical Reviews (MathSciNet): MR88d:32018
Zentralblatt MATH: 0656.32005
[Lê3] D. T. Lê, Morsification of $\mathcalD$-modules, preprint, 1988.
[Lê4] Lê D. T., Sur les cycles évanouissants des espaces analytiques, C. R. Acad. Sci. Paris Sér. A-B 288 (1979), no. 4, A283–A285.
Mathematical Reviews (MathSciNet): MR80i:32030
Zentralblatt MATH: 0471.32007
[Lê5] D. T. Lê, Topological use of polar curves, Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29, Humboldt State Univ., Arcata, Calif., 1974), Amer. Math. Soc., Providence, R.I., 1975, pp. 507–512.
Mathematical Reviews (MathSciNet): MR51:10681
Zentralblatt MATH: 0323.14003
[Lê6] D. T. Lê, Une application d'un théorème d'A'Campo à l'équisingularité, Nederl. Akad. Wetensch. Proc. Ser. A 76 =Indag. Math. 35 (1973), 403–409.
Mathematical Reviews (MathSciNet): MR48:4347
Zentralblatt MATH: 0271.14001
[LM] D. T. Lê and Z. Mebkhout, Variétés caractéristiques et variétés polaires, C. R. Acad. Sci. Paris Sér. I Math. 296 (1983), no. 2, 129–132.
Mathematical Reviews (MathSciNet): MR84g:32018
Zentralblatt MATH: 0566.32020
[LT1] D. T. Lê and B. Teissier, Cycles evanescents, sections planes et conditions de Whitney. II, Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 65–103.
Mathematical Reviews (MathSciNet): MR86c:32005
Zentralblatt MATH: 0532.32003
[LT2] D. T. Lê and B. Teissier, Variétés polaires locales et classes de Chern des variétés singulières, Ann. of Math. (2) 114 (1981), no. 3, 457–491.
Mathematical Reviews (MathSciNet): MR83k:32012a
Zentralblatt MATH: 0488.32004
Digital Object Identifier: doi:10.2307/1971299
JSTOR: links.jstor.org
[Lo] E. J. N. Looijenga, Isolated Singular Points on Complete Intersections, London Math. Soc. Lecture Note Ser., vol. 77, Cambridge Univ. Press, Cambridge, 1984.
Mathematical Reviews (MathSciNet): MR86a:32021
Zentralblatt MATH: 0552.14002
[Mac1] R. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432.
Mathematical Reviews (MathSciNet): MR50:13587
Zentralblatt MATH: 0311.14001
Digital Object Identifier: doi:10.2307/1971080
JSTOR: links.jstor.org
[Mac2] R. MacPherson, Global questions in the topology of singular spaces, Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Warsaw, 1983), PWN, Warsaw, 1984, pp. 213–235.
Mathematical Reviews (MathSciNet): MR86m:58016
Zentralblatt MATH: 0612.57012
[Mas1] D. Massey, Calculations on hypersurface singularities, preprint, 1992.
[Mas2] D. Massey, The characteristic polar cycles of a perverse sheaf, preprint, 1990.
[Mas3] D. Massey, A general calculation of the number of vanishing cycles, preprint, 1992.
Mathematical Reviews (MathSciNet): MR1318426
Zentralblatt MATH: 0824.32013
Digital Object Identifier: doi:10.1016/0166-8641(94)00042-2
[Mas4] D. Massey, The Lê varieties, I, Invent. Math. 99 (1990), no. 2, 357–376.
Mathematical Reviews (MathSciNet): MR91a:32053
Zentralblatt MATH: 0712.32020
Digital Object Identifier: doi:10.1007/BF01234423
[Mas5] D. Massey, The Lê varieties, II, Invent. Math. 104 (1991), no. 1, 113–148.
Mathematical Reviews (MathSciNet): MR92c:32049
Zentralblatt MATH: 0727.32015
Digital Object Identifier: doi:10.1007/BF01245068
[Mas6] D. Massey, Local Morse inequalities and perverse sheaves, preprint, 1990.
[Mas7] D. Massey, The Thom condition along a line, Duke Math. J. 60 (1990), no. 3, 631–642.
Mathematical Reviews (MathSciNet): MR91f:32047
Zentralblatt MATH: 0709.32026
Digital Object Identifier: doi:10.1215/S0012-7094-90-06025-9
Project Euclid: euclid.dmj/1077297440
[Mat] J. Mather, Notes on topological stability, unpublished notes, Harvard Univ., 1970.
[Meb] Z. Mebkhout, Local cohomology of analytic spaces, Publ. Res. Inst. Math. Sci. 12 (1976/77), no. supplement, 247–256.
Mathematical Reviews (MathSciNet): MR56:12307
Zentralblatt MATH: 0372.32007
Digital Object Identifier: doi:10.2977/prims/1195196607
[Mer] M. Merle, Variétés polaires, stratifications de Whitney et classes de Chern des espaces analytiques complexes (d'après Lê-Teissier), Bourbaki seminar, Vol. 1982/83, Astérisque, vol. 105, Soc. Math. France, Paris, 1983, pp. 65–78.
Mathematical Reviews (MathSciNet): MR85a:32011
Zentralblatt MATH: 0551.32011
[Mi] J. Milnor, Singular Points of Complex Hypersurfaces, Ann. of Math. Stud., vol. 61, Princeton Univ. Press, Princeton, 1968.
Mathematical Reviews (MathSciNet): MR39:969
Zentralblatt MATH: 0184.48405
[OS] P. Orlik and L. Solomon, Combinatorics and topology of complements of hyperplanes, Invent. Math. 56 (1980), no. 2, 167–189.
Mathematical Reviews (MathSciNet): MR81e:32015
Zentralblatt MATH: 0432.14016
Digital Object Identifier: doi:10.1007/BF01392549
[OT] P. Orlik and H. Terao, Arrangements of Hyperplanes, Grundlehren Math. Wiss., vol. 300, Springer-Verlag, Berlin, 1992.
Mathematical Reviews (MathSciNet): MR94e:52014
Zentralblatt MATH: 0757.55001
[Sab1] C. Sabbah, Proximité évanescente. I. La structure polaire d'un $\scr D$-module, Compositio Math. 62 (1987), no. 3, 283–328.
Mathematical Reviews (MathSciNet): MR90a:32014
Zentralblatt MATH: 0622.32012
[Sab2] C. Sabbah, Quelques remarques sur la géométrie des espaces conormaux, Astérisque (1985), no. 130, 161–192.
Mathematical Reviews (MathSciNet): MR87f:32031
Zentralblatt MATH: 0598.32011
[Sai] M. Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), no. 2, 221–333.
Mathematical Reviews (MathSciNet): MR91m:14014
Zentralblatt MATH: 0727.14004
Digital Object Identifier: doi:10.2977/prims/1195171082
[ST] P. Schapira and N. Tose, Morse inequalities for $R$-constructible sheaves, to appear in Adv. Math.
Mathematical Reviews (MathSciNet): MR1160840
Zentralblatt MATH: 0767.58008
Digital Object Identifier: doi:10.1016/0001-8708(92)90022-D
[Si] D. Siersma, Isolated line singularities, Singularities, Part 2 (Arcata, Calif., 1981), Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, 1983, pp. 485–496.
Mathematical Reviews (MathSciNet): MR85d:32017
Zentralblatt MATH: 0514.32007
[Te1] B. Teissier, Variétés polaires. I. Invariants polaires des singularités d'hypersurfaces, Invent. Math. 40 (1977), no. 3, 267–292.
Mathematical Reviews (MathSciNet): MR57:10004
Zentralblatt MATH: 0446.32002
Digital Object Identifier: doi:10.1007/BF01425742
[Te2] B. Teissier, Variétés polaires II: Multiplicités polaires, sections planes, et conditions de Whitney, Algebraic Geometry (La Rábida, 1981), Lecture Notes in Math., vol. 961, Springer-Verlag, Berlin, 1982, pp. 314–491.
Mathematical Reviews (MathSciNet): MR85i:32019
Zentralblatt MATH: 0585.14008
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