Sols Lucía, IgnacioHermoso, Carlos2023-06-202023-06-2019960214-3577https://hdl.handle.net/20.500.14352/58403For 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 ].engjournal articlehttp://www.mat.ucm.es/serv/revmat/vol9-1/vol9-1b.pdfhttp://www.mat.ucm.es/serv/revmat/p_home_in.htmrestricted access512Bases for rational homology groupHilbert schemeZero-dimensional subschemesEnumerative geometryÁlgebra1201 Álgebra