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Sols, Ignacio and Hermoso, Carlos
(1996)
*Bases of the homology spaces of the Hilbert scheme of points in an algebraic surface.*
Revista matemática de la Universidad Complutense de Madrid, 9
(1).
pp. 53-66.
ISSN 0214-3577

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Official URL: http://www.mat.ucm.es/serv/revmat/vol9-1/vol9-1b.pdf

## Abstract

For a complex surface S , proper, smooth and connected, the authors find two bases of the spaces of rational homology H n (Hilb d S) Q of the Hilbert scheme of subschemes of S of length d . The idea of the proof of the main theorem is to prove that the elements of the two candidates have as cardinalities the known Betti numbers of Hilb d S and to show that both intersect in a triangular matrix of nonzero diagonal entries. Papers on the subject which have a close connection with the present one are by B. Fantechi ["Base of the homology groups of the Hilbert scheme of points on a surface'', Preprint; per bibl.] and L. Göttsche [Math. Ann. 286 (1990), no. 1-3, 193–207

].

Item Type: | Article |
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Uncontrolled Keywords: | Bases for rational homology group; Hilbert scheme; Zero-dimensional subschemes; Enumerative geometry |

Subjects: | Sciences > Mathematics > Algebra |

ID Code: | 20880 |

Deposited On: | 16 Apr 2013 16:23 |

Last Modified: | 19 Feb 2019 12:55 |

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