GC4M

Generalized complex 4-manifolds

 Coordinatore UNIVERSITEIT UTRECHT 

 Organization address address: Heidelberglaan 8
city: UTRECHT
postcode: 3584 CS

contact info
Titolo: Prof.
Nome: Eduard
Cognome: Looijenga
Email: send email
Telefono: 31302531535
Fax: 31302518394

 Nazionalità Coordinatore Netherlands [NL]
 Totale costo 157˙831 €
 EC contributo 157˙831 €
 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-2007-2-1-IEF
 Funding Scheme MC-IEF
 Anno di inizio 2009
 Periodo (anno-mese-giorno) 2009-06-01   -   2011-05-31

 Partecipanti

# participant  country  role  EC contrib. [€] 
1    UNIVERSITEIT UTRECHT

 Organization address address: Heidelberglaan 8
city: UTRECHT
postcode: 3584 CS

contact info
Titolo: Prof.
Nome: Eduard
Cognome: Looijenga
Email: send email
Telefono: 31302531535
Fax: 31302518394

NL (UTRECHT) coordinator 0.00

Mappa

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 Word cloud

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

generalized    ginzburg    manifold    landau    lefschetz    structure    symmetry    mirror    question    torus    fibrations    pencil    models    symplectic    structures    mdash    pencils    setting    manifolds   

 Obiettivo del progetto (Objective)

'We will study a notion of Lefschetz pencils for generalized complex 4-manifolds, aiming at results analogue to those of Donalson and Gompf in symplectic geometry stating that a 4-manifold has a symplectic structure if and only if it admits a Lefschetz pencil. To achieve the desired results we have to find the right definition of a Lefschetz pencil in the generalized complex setting. Earlier work of the candidate on this area has already shed some light into this question. We will study the question of how to adapt Seiberg—Witten theory in order to produce differential—topological obstructions for a 4-manifold to admit a generalized complex structure. This should mirror Taubes' result relating SW-invariants and symplectic structures. Work of Bauer and Furuta should provide the springboard for this part of the project. On the physical side, we will study mirror symmetry on generalized complex manifolds. The work on Lefschetz pencils will provide us with a number of generalized complex manifolds described in terms of singular torus fibrations, therefore an ideal place where to study mirror symmetry in the setting of SYZ. For these torus fibrations, there is a locus on the base where one of the circles forming the torus fiber collapses. In other models where this occurs, one describes the mirror as a Landau—Ginzburg model. Therefore this raises the questions about what Landau—Ginzburg models are for generalized structures.'

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