The Michigan Mathematical Journal

Hodge polynomials of singular hypersurfaces

Anatoly Libgober and Laurentiu Maxim

Full-text: Open access

Article information

Source
Michigan Math. J., Volume 60, Issue 3 (2011), 661-673.

Dates
First available in Project Euclid: 8 November 2011

Permanent link to this document
https://projecteuclid.org/euclid.mmj/1320763053

Digital Object Identifier
doi:10.1307/mmj/1320763053

Mathematical Reviews number (MathSciNet)
MR2861093

Zentralblatt MATH identifier
1229.32019

Subjects
Primary: 32S25: Surface and hypersurface singularities [See also 14J17] 32S35: Mixed Hodge theory of singular varieties [See also 14C30, 14D07] 57R20: Characteristic classes and numbers
Secondary: 14D07: Variation of Hodge structures [See also 32G20] 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 34M35: Singularities, monodromy, local behavior of solutions, normal forms

Citation

Libgober, Anatoly; Maxim, Laurentiu. Hodge polynomials of singular hypersurfaces. Michigan Math. J. 60 (2011), no. 3, 661--673. doi:10.1307/mmj/1320763053. https://projecteuclid.org/euclid.mmj/1320763053


Export citation

References

  • N. A'Campo, La fonction zêta d'une monodromie, Comment. Math. Helv. 50 (1975), 233–248.
  • A. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Analysis and topology on singular spaces, I (Luminy, 1981), Astérisque 100 (1982), 5–171.
  • P. Brasselet, J. Schürmann, and S. Yokura, Hirzebruch classes and motivic Chern classes for singular spaces, J. Topol. Anal. 2 (2010), 1–55.
  • J. W. Bruce and C. T. C. Wall, On the classification of cubic surfaces, J. London Math. Soc. (2) 19 (1979), 245–256.
  • S. E. Cappell, A. Libgober, L. Maxim, and J. L. Shaneson, Hodge genera and characteristic classes of complex algebraic varieties, Electron. Res. Announc. Amer. Math. Sci. 15 (2008), 1–7.
  • –––, Hodge genera of algebraic varieties, II, Math. Ann. 345 (2009), 925–972.
  • S. E. Cappell, L. Maxim, J. Schürmann, and J. L. Shaneson, Characteristic classes of complex hypersurfaces, Adv. Math. 225 (2010), 2616–2647.
  • P. Deligne, Théorie de Hodge, II, Inst. Hautes Études Sci. Publ. Math. 40 (1971), 5–57.
  • –––, Le formalisme des cycles évanescents, SGA VII, Exp. XIII, Lecture Notes in Math., 340, pp. 82–115, Springer-Verlag, Berlin, 1973.
  • –––, Théorie de Hodge, III, Inst. Hautes Études Sci. Publ. Math. 44 (1974), 5–77.
  • A. Dimca, Hodge numbers of hypersurfaces, Abh. Math. Sem. Univ. Hamburg 66 (1996), 377–386.
  • –––, Sheaves in topology, Springer-Verlag, Berlin, 2004.
  • A. Dimca and G. I. Lehrer, Purity and equivariant weight polynomials, Algebraic groups and Lie groups, Austral. Math. Soc. Lect. Ser., 9, pp. 161–181, Cambridge Univ. Press, Cambridge, 1997.
  • W. Fulton and K. Johnson, Canonical classes on singular varieties, Manuscripta Math. 32 (1980), 381–389.
  • F. Hirzebruch, Topological methods in algebraic geometry, Springer-Verlag, New York, 1966.
  • S. Kleiman, The enumerative theory of singularities, Real and complex singularities (Oslo, 1976), pp. 297–396, Sijthoff & Noordhoff, Alphen aan den Rijn, 1977.
  • R. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432.
  • V. Navarro Aznar, Sur les structures de Hodge mixtes associées aux cycles évanescents, Hodge theory (Sant Cugat, 1985), Lecture Notes in Math., 1246, pp. 143–153, Springer-Verlag, Berlin, 1987.
  • –––, Sur la théory de Hodge–Deligne, Invent. Math. 90 (1987), 11–76.
  • A. Parusiński, A generalization of the Milnor number, Math. Ann. 281 (1988), 247–254.
  • A. Parusiński and P. Pragacz, A formula for the Euler characteristic of singular hypersurfaces, J. Algebraic Geom. 4 (1995), 337–351.
  • –––, Characteristic classes of hypersurfaces and characteristic cycles, J. Algebraic Geom. 10 (2001), 63–79.
  • C. Peters and J. Steenbrink, Mixed Hodge structures, Ergeb. Math. Grenzgeb. (3), 52, Springer-Verlag, Berlin, 2008.
  • M. Saito, Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci. 24 (1988), 849–995.
  • –––, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), 221–333.
  • J. Schürmann, Lectures on characteristic classes of constructible functions, Trends Math., pp. 175–201, Birkhäuser, Basel, 2005.
  • –––, A generalized Verdier-type Riemann–Roch theorem for Chern–Schwartz–MacPherson classes, preprint, arXiv:math/0202175.
  • S. Yokura, On characteristic classes of complete intersections, Algebraic geometry: Hirzebruch 70 (Warsaw, 1998), Contemp. Math., 241, pp. 349–369, Amer. Math. Soc., Providence, RI, 1999.