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Bases of the homology spaces of the Hilbert scheme of points in an algebraic surface

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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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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
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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