The Michigan Mathematical Journal

Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points

S. M. Gusein-Zade,I. Luengo, and A. Melle-Hernández

Full-text: Open access

Article information

Source
Michigan Math. J. Volume 54, Issue 2 (2006), 353-359.

Dates
First available: 23 August 2006

Permanent link to this document
http://projecteuclid.org/euclid.mmj/1156345599

Digital Object Identifier
doi:10.1307/mmj/1156345599

Zentralblatt MATH identifier
1122.14003

Mathematical Reviews number (MathSciNet)
MR2252764

Subjects
Primary: 14A20: Generalizations (algebraic spaces, stacks) 14C05: Parametrization (Chow and Hilbert schemes) 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture)

Citation

Gusein-Zade, S. M.; Luengo, I.; Melle-Hernández, A. Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points. The Michigan Mathematical Journal 54 (2006), no. 2, 353--359. doi:10.1307/mmj/1156345599. http://projecteuclid.org/euclid.mmj/1156345599.


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References

  • J. Burillo, The Poincaré--Hodge polynomial of a symmetric product of compact Kähler manifolds, Collect. Math. 41 (1990), 59--69.
  • A. Campillo, F. Delgado, and S. M. Gusein-Zade, The Alexander polynomial of a plane curve singularity via the ring of functions on it, Duke Math. J. 117 (2003), 125--156.
  • M. A. de Cataldo, Hilbert schemes of a surface and Euler characteristics, Arch. Math. (Basel) 75 (2000), 59--64.
  • J. Cheah, On the cohomology of Hilbert schemes of points, J. Algebraic Geom. 5 (1996), 479--511.
  • G. Ellingsrud and S. A. Strømme, On a cell decomposition of the Hilbert scheme of points in the plane, Invent. Math. 91 (1988), 365--370.
  • E. Getzler, Mixed Hodge structures of configuration spaces, preprint, ArXiv math.AG/9510018.
  • L. Göttsche, The Betti numbers of the Hilbert scheme of points on a smooth projective surface, Math. Ann. 286 (1990), 193--207.
  • ------, On the motive of the Hilbert scheme of points on a surface, Math. Res. Lett. 8 (2001), 613--627.
  • L. Göttsche and W. Soergel, Perverse sheaves and the cohomology of Hilbert schemes of smooth algebraic surfaces, Math. Ann. 296 (1993), 235--245.
  • S. M. Gusein-Zade, I. Luengo, and A. Melle-Hernández, A power structure over the Grothendieck ring of varieties, Math. Res. Lett. 11 (2004), 49--57.
  • M. Kapranov, The elliptic curve in the $S$-duality theory and Eisenstein series for Kac--Moody groups, preprint, ArXiv math.AG/0001005.
  • D. Knutson, $\lambda$-rings and the representation theory of the symmetric group, Lecture Notes in Math., 308, Springer-Verlag, Berlin, 1973.
  • I. G. Macdonald, The Poincaré polynomial of a symmetric product, Proc. Cambridge Philos. Soc. 58 (1962), 563--568.