Advertisement

Characteristic Classes of Singular Varieties

  • Paolo Aluffi
Chapter
Part of the Trends in Mathematics book series (TM)

Keywords

Line Bundle Characteristic Classis Chern Class Exceptional Divisor Characteristic Cycle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AC93]
    Paolo Aluffi and Fernando Cukierman. Multiplicities of discriminants. Manuscripta Math., 78(3):245–258, 1993.Google Scholar
  2. [AF93]
    Paolo Aluffi and Carel Faber. Linear orbits of d-tuples of points in p1. J. Reine Angew. Math., 445:205–220, 1993.Google Scholar
  3. [Alu94]
    Paolo Aluffi. MacPherson’s and Fulton’s Chern classes of hypersurfaces. Internat. Math. Res. Notices, (11):455–465, 1994.CrossRefGoogle Scholar
  4. [Alu95]
    Paolo Aluffi. Singular schemes of hypersurfaces. Duke Math. J., 80(2):325–351, 1995.CrossRefGoogle Scholar
  5. [Alu98]
    Paolo Aluffi. Characteristic classes of discriminants and enumerative geometry. Comm. Algebra, 26(10):3165–3193, 1998.Google Scholar
  6. [Alu99a]
    Paolo Aluffi. Chern classes for singular hypersurfaces. Trans. Amer. Math. Soc., 351(10):3989–4026, 1999.CrossRefGoogle Scholar
  7. [Alu99b]
    Paolo Aluffi. Differential forms with logarithmic poles and Chern-Schwartz-MacPherson classes of singular varieties. C. R. Acad. Sci. Paris Sér. I Math., 329(7):619–624, 1999.Google Scholar
  8. [Alu00]
    Paolo Aluffi. Weighted Chern-Mather classes and Milnor classes of hypersurfaces. In Singularities — Sapporo 1998, pages 1–20. Kinokuniya, Tokyo, 2000.Google Scholar
  9. [Alu02]
    Paolo Aluffi. Shadows of blow-up algebras. Tohoku Math. J. (2) 56 (2004), no. 4, 593–619.MathSciNetGoogle Scholar
  10. [Alu03a]
    Paolo Aluffi. Computing characteristic classes of projective schemes. J. Symbolic Comput., 35(1):3–19, 2003.CrossRefGoogle Scholar
  11. [Alu03b]
    Paolo Aluffi. Inclusion-exclusion and Segre classes. Comm. Algebra, 31(8):3619–3630, 2003. Special issue in honor of Steven L. Kleiman.CrossRefGoogle Scholar
  12. [Alu03c]
    Paolo Aluffi. Inclusion-exclusion and Segre classes. II. In Topics in algebraic and noncommutative geometry (Luminy/Annapolis, MD. 2001), volume 324 of Contemp. Math., pages 51–61. Amer. Math. Soc., Providence, RI, 2003.Google Scholar
  13. [BLSS02]
    J.-P. Brasselet, D. Lehmann, J. Seade, and T. Suwa. Milnor classes of local complete intersections. Trans. Amer. Math. Soc., 354(4):1351–1371 (electronic), 2002.CrossRefGoogle Scholar
  14. [Bra00]
    Jean-Paul Brasselet. From Chern classes to Milnor classes — a history of characteristic classes for singular varieties. In Singularities — Sapporo 1998, pages 31–52. Kinokuniya, Tokyo, 2000.Google Scholar
  15. [BS81]
    J.-P. Brasselet and M.-H. Schwartz. Sur les classes de Chern d’un ensemble analytique complex. In The Euler-Poincaré characteristic (French), pages 93–147. Soc. Math. France, Paris, 1981.Google Scholar
  16. [Ful84]
    William Fulton. Intersection theory. Springer-Verlag, Berlin, 1984.Google Scholar
  17. [GP02]
    Mark Goresky and William Pardon. Chern classes of automorphic vector bundles. Invent. Math., 147:561–612, 2002.CrossRefGoogle Scholar
  18. [ReS]
    A. Grothendieck, Récoltes et Semailles; Réflexions et Témoignages sur un passé de mathématicien, Reprint, Université des Sciences et Techniques du Languedoc (Montpellier) et CNRS, 1985.Google Scholar
  19. [Ken90]
    Gary Kennedy. MacPherson’s Chern classes of singular algebraic varieties. Comm. Algebra, 18(9):2821–2839, 1990.Google Scholar
  20. [Kwi94]
    Michal Kwieciński. Sur le transformé de Nash et la construction du graphe de MacPherson. PhD thesis, Université de Provence (Aix-Marseille I), 1994.Google Scholar
  21. [Mac74]
    R.D. MacPherson. Chern classes for singular algebraic varieties. Ann. of Math. (2), 100:423–432, 1974.Google Scholar
  22. [Par88]
    Adam Parusiński. A generalization of the Milnor number. Math. Ann., 281(2):247–254, 1988.CrossRefGoogle Scholar
  23. [PP01]
    Adam Parusiński and Piotr Pragacz. Characteristic classes of hypersurfaces and characteristic cycles. J. Algebraic Geom., 10(1):63–79, 2001.Google Scholar
  24. [Sab85]
    C. Sabbah. Quelques remarques sur la géométrie des spaces conormaux. Astérisque, (130):161–192, 1985. Differential systems and singularities (Luminy, 1983).Google Scholar
  25. [Sch82]
    Marie-Hé1ène Schwartz. Classes et caractères de Chern-Mather des spaces linèaires. C. R. Acad. Sci. Paris Sér. I Math., 295(5):399–402, 1982.Google Scholar

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Paolo Aluffi
    • 1
    • 2
  1. 1.Max-Planck-Institut für MathematikBonnGermany
  2. 2.Florida State UniversityTallahasseeUSA

Personalised recommendations