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. Fields of science engineering and technologymaterials engineeringfibersnatural sciencesmathematicspure mathematicstopologysymplectic topologynatural sciencesmathematicspure mathematicsgeometry Keywords Lefschetz pencils Seiberg-Witten invariants generalized complex structures mirror symmetry Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Topic(s) PEOPLE-2007-2-1.IEF - Marie Curie Action: "Intra-European Fellowships for Career Development" Call for proposal FP7-PEOPLE-2007-2-1-IEF See other projects for this call Funding Scheme MC-IEF - Intra-European Fellowships (IEF) Coordinator UNIVERSITEIT UTRECHT EU contribution € 157 831,18 Address HEIDELBERGLAAN 8 3584 CS Utrecht Netherlands See on map Region West-Nederland Utrecht Utrecht Activity type Higher or Secondary Education Establishments Administrative Contact Eduard Looijenga (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
