Advertisement

Perverse Sheaves

  • Laurenţiu G. Maxim
Chapter
Part of the Graduate Texts in Mathematics book series (GTM, volume 281)

Abstract

Perverse sheaves are fundamental objects of study in topology, algebraic geometry, analysis and differential equations, with a plethora of applications, including in adjacent fields such as number theory, representation theory, combinatorics and algebra. In this chapter, we overview the relevant definitions and results of the theory of perverse sheaves, with an emphasis on examples and applications (see also Chapters  9 and  10 for more applications of perverse sheaves).

References

  1. 6.
    Banagl, M.: Topological Invariants of Stratified Spaces. Springer Monographs in Mathematics. Springer, Berlin (2007)Google Scholar
  2. 12.
    Beı̆linson, A.A., Bernstein, J.N., Deligne, P.: Faisceaux pervers. In: Analysis and Topology on Singular Spaces, I (Luminy, 1981). Astérisque, vol. 100, pp. 5–171. Soc. Math. France, Paris (1982)Google Scholar
  3. 49.
    de Cataldo, M.A.A., Migliorini, L.: The Hodge theory of algebraic maps. Ann. Sci. École Norm. Sup. (4) 38(5), 693–750 (2005)Google Scholar
  4. 51.
    de Cataldo, M.A.A., Migliorini, L.: The decomposition theorem, perverse sheaves and the topology of algebraic maps. Bull. Amer. Math. Soc. (N.S.) 46(4), 535–633 (2009)MathSciNetCrossRefGoogle Scholar
  5. 52.
    de Cataldo, M.A.A., Migliorini, L.: What is… a perverse sheaf? Notices Amer. Math. Soc. 57(5), 632–634 (2010)MathSciNetzbMATHGoogle Scholar
  6. 60.
    Dimca, A.: Singularities and Topology of Hypersurfaces. Universitext. Springer, New York (1992)CrossRefGoogle Scholar
  7. 61.
    Dimca, A.: Sheaves in Topology. Universitext. Springer, Berlin (2004)CrossRefGoogle Scholar
  8. 83.
    Goresky, M., MacPherson, R.: Intersection homology. II. Invent. Math. 72(1), 77–129 (1983)MathSciNetCrossRefGoogle Scholar
  9. 94.
    Hamm, H.: Lokale topologische Eigenschaften komplexer Räume. Math. Ann. 191, 235–252 (1971)MathSciNetCrossRefGoogle Scholar
  10. 96.
    Hamm, H.: Zum Homotopietyp q-vollständiger Räume. J. Reine Angew. Math. 364, 1–9 (1986)MathSciNetzbMATHGoogle Scholar
  11. 107.
    Hotta, R., Takeuchi, K., Tanisaki, T.: D-modules, Perverse Sheaves, and Representation Theory. Progress in Mathematics, vol. 236. Birkhäuser Boston, Inc., Boston, MA (2008). Translated from the 1995 Japanese edition by TakeuchiGoogle Scholar
  12. 115.
    Karčjauskas, K.: A generalized Lefschetz theorem. Funkcional. Anal. i Priložen. 11(4), 80–81 (1977)MathSciNetGoogle Scholar
  13. 118.
    Kashiwara, M.: Faisceaux constructibles et systèmes holonômes d’équations aux dérivées partielles linéaires à points singuliers réguliers. In: Séminaire Goulaouic-Schwartz, 1979–1980 (French) pages Exp. No. 19, 7. École Polytech., Palaiseau (1980)Google Scholar
  14. 119.
    Kashiwara, M.: The Riemann-Hilbert problem for holonomic systems. Publ. Res. Inst. Math. Sci. 20(2), 319–365 (1984)MathSciNetCrossRefGoogle Scholar
  15. 122.
    Kashiwara, M., Schapira, P.: Sheaves on manifolds. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292. Springer, Berlin (1994)Google Scholar
  16. 129.
    Kleiman, S.L.: The development of intersection homology theory. Pure Appl. Math. Q. 3(1, Special Issue: In honor of Robert D. MacPherson. Part 3), 225–282 (2007)MathSciNetCrossRefGoogle Scholar
  17. 133.
    Lazarsfeld, R.: Positivity in Algebraic Geometry. I. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 28. Springer, Berlin (2004). Classical setting: line bundles and linear seriesGoogle Scholar
  18. 138.
    Lê, D.T.: Sur les cycles évanouissants des espaces analytiques. C. R. Acad. Sci. Paris Sér. A-B 288(4), A283–A285 (1979)zbMATHGoogle Scholar
  19. 172.
    Mebkhout, Z.: Sur le problème de Hilbert-Riemann. In: Complex analysis, microlocal calculus and relativistic quantum theory (Proc. Internat. Colloq., Centre Phys., Les Houches, 1979). Lecture Notes in Physics, vol. 126, pp. 90–110. Springer, Berlin/New York (1980)Google Scholar
  20. 173.
    Mebkhout, Z.: Une autre équivalence de catégories. Compos. Math. 51(1), 63–88 (1984)MathSciNetzbMATHGoogle Scholar
  21. 214.
    Schürmann, J.: Topology of Singular Spaces and Constructible Sheaves. Monografie Matematyczne, vol. 63. Birkhäuser Verlag, Basel (2003)CrossRefGoogle Scholar
  22. 228.
    Théorie des topos et cohomologie étale des schémas. Tome 3. Lecture Notes in Mathematics, vol. 305. Springer, Berlin/New York (1973). Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4), Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de P. Deligne et B. Saint-DonatGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Laurenţiu G. Maxim
    • 1
  1. 1.Department of MathematicsUniversity of Wisconsin-MadisonMadisonUSA

Personalised recommendations