Deformations in the large of some complex manifolds, I
| dc.creator | Catanese, Fabrizio | |
| dc.date | 2003-07-04 | |
| dc.date.accessioned | 2026-07-07T04:59:26Z | |
| dc.date.available | 2026-07-07T04:59:26Z | |
| dc.description | Main topic of the paper is the determination, for a compact complex manifold $M$, of the class of manifolds $X$ which are deformation equivalent to it. If $M$ is a complex torus, then also $X$ is so. After describing the structure of principal holomorphic torus bundles over curves, a similar result (stability by deformations in the large) is obtained also for the latter class of manifolds. A section of the paper is devoted to the structure of principal holomorphic torus bundles over tori, establishing the Riemann bilinear relations, and exhibiting a so called Appell Humbert family, which could conjecturally give all small deformations. Finally, a general definition is given of so called Blanchard -Calabi manifolds, which, using an old construction of Sommese, show that the family of complex structures on the differentiable manifold underlying the product of a curve of genus $g\geq 2$ with a 2-dimensional complex torus admits several distinct deformation types. | |
| dc.description | 29 pages, to appear in Annali di Mat. pura e appl., volume in memory of Fabio Bardelli | |
| dc.identifier | https://arxiv.org/abs/math/0307067 | |
| dc.identifier | http://arxiv.org/abs/math/0307067 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67982 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32G08, 32G05, 14J15,32G13 | |
| dc.title | Deformations in the large of some complex manifolds, I | |
| dc.type | text |