### Impacto

Gusein-Zade, Sabir Medgidovich and Luengo Velasco, Ignacio and Melle Hernández, Alejandro
(2006)
*Power structure over the Grothendieck ring of varieties and generating series of Hilbert schemes of points.*
Michigan Mathematical Journal, 54
(2).
pp. 353-359.
ISSN 0026-2285

PDF
Restringido a Repository staff only hasta 31 December 2020. 85kB |

Official URL: http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.mmj/1156345599

## Abstract

The power structure over the Grothendieck (semi)ring of complex quasi-projective varieties constructed by the authors is used to express the generating series of classes of Hilbert schemes of zero-dimensional subschemes on a smooth quasi-projective variety as an exponent of that for the complex affine space of the same dimension. Specializations of this relation give formulae for generating series of such invariants of the Hilbert schemes of points as the Euler characteristic and the Hodge-Deligne polynomial.

Item Type: | Article |
---|---|

Additional Information: | The first author was partially supported by the grants RFBR-04-01-00762, NSh-1972.2003.1. The last two authors were partially supported by the grant BFM2001-1488-C02-01. |

Uncontrolled Keywords: | Surface; Plane |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 16602 |

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, λ-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. |

Deposited On: | 03 Oct 2012 08:18 |

Last Modified: | 07 Feb 2014 09:32 |

Repository Staff Only: item control page