DEFFOL

"Complex manifolds, foliations by complex leaves and their deformations"

Coordinatore	Consorci Centre de Recerca Matematica    more  Organization address address: FACULTAD CIENCIES UAB APRATADO 50 city: BELLATERRA postcode: 8193 contact info Titolo: Mrs. Nome: Ana Cognome: García-Donas Email: send email Telefono: 34935812953
Nazionalità Coordinatore	Spain [ES]
Totale costo	223˙280 €
EC contributo	223˙280 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2010-IEF
Funding Scheme	MC-IEF
Anno di inizio	2011
Periodo (anno-mese-giorno)	2011-09-01   -   2013-08-31

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	Consorci Centre de Recerca Matematica  Organization address address: FACULTAD CIENCIES UAB APRATADO 50 city: BELLATERRA postcode: 8193 contact info Titolo: Mrs. Nome: Ana Cognome: García-Donas Email: send email Telefono: 34935812953	ES (BELLATERRA)	coordinator	223˙280.00

Mappa

 Word cloud

Esplora la "nuvola delle parole (Word Cloud) per avere un'idea di massima del progetto.

 Obiettivo del progetto (Objective)

'My proposal is to investigate some new aspects of the geometry of complex manifolds, foliations by complex leaves and their deformations. Emphasis is put on the relations between these three themes.

The basic objects of complex geometry are compact complex manifolds. However, only very special classes are well understood. And the only theory which applies to the general case is Kodaira-Spencer theory of deformations. To each structure of a compact complex manifold it associates a finite-dimensional space, called Kuranishi space, containing all the small deformations of this initial structure. Although it is a very classical theory, almost nothing is known about the geometry of this space. Last year, I discovered that it has a natural foliated structure and I want to study it more thoroughly.

On the other hand, Kuranishi spaces exist for transversely holomorphic foliations, which form a generalization of complex structures. There is however another natural generalization, that of foliation by complex leaves. Now in this case there is no Kuranishi space (the finite-dimensionality fails). I have some precise ideas to construct (finite-dimensional) Kuranishi spaces in a generalized sense.

Finally I also want to introduce a notion of geometric rigidity, which is better adapted to the case of a foliation than the classical notion of rigidity.

As a researcher, I work for twelve years on the geometry and topology of compact complex manifolds. But to achieve these goals, I need to strengthen my training in deformation theory. So I plan to spend two years at CRM, Barcelona, under the guidance of Marcel Nicolau, an expert in deformations of complex manifolds and transversely holomorphic foliations. I could also benefit from the intense mathematical activity of the CRM, especially in complex analysis and geometry.

Achieving these goals would open new lines of research and qualify me as a leading expert in the field. Last but not least, I could look for another position.'