The Douady space of a complex surface
| dc.creator | de Cataldo, Mark Andrea A. | |
| dc.creator | Migliorini, Luca | |
| dc.date | 1998-11-27 | |
| dc.date.accessioned | 2026-07-07T05:27:00Z | |
| dc.date.available | 2026-07-07T05:27:00Z | |
| dc.description | We prove that a standard realization of the direct image complex via the so-called Douady-Barlet morphism associated with a smooth complex analytic surface admits a natural decomposition in the form of an injective quasi-isomorphism of complexes. This is a more precise form of a special case of the decomposition theorems of Beilinson-Bernstein-Deligne-Gabber and M. Saito. The proof hinges on the special case of the bi-disk in the complex affine plane where we make explicit use of a construction of Nakajima's and of the corresponding representation-theoretic interpretation foreseen by Vafa-Witten. Some consequences of the decomposition theorem: Göttsche Formula holds for complex surfaces; interpretation of the rational cohomologies of Douady spaces as a kind of Fock space; new proofs of results of Briançon and Ellingsrud-Stromme on punctual Hilbert schemes; computation of the mixed Hodge structure of the Douady spaces in the Kähler case. We also derive a natural connection with Equivariant K-Theory for which, in the case of algebraic surfaces, Bezrukavnikov-Ginzburg have proposed a different approach. | |
| dc.description | Latex; 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/9811159 | |
| dc.identifier | http://arxiv.org/abs/math/9811159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/77765 | |
| dc.subject | Algebraic Geometry | |
| dc.title | The Douady space of a complex surface | |
| dc.type | text |