par Behrens, Stefan;Cavalcanti, Gil Ramos;Klaasse, Ralph 
Référence Geometry and Physics: A Festschrift in Honour of Nigel Hitchin, Oxford University Press, Vol. 2, page (399-418)
Publication Publié, 2018-01
Référence Geometry and Physics: A Festschrift in Honour of Nigel Hitchin, Oxford University Press, Vol. 2, page (399-418)
Publication Publié, 2018-01
Partie d'ouvrage collectif
| Résumé : | Stable generalized complex structures can be constructed out of boundary Lefschetz fibrations. On 4-manifolds, these are essentially genus one Lefschetz fibrations over surfaces, except that generic fibres can collapse to circles over a codimension 1 submanifold, which is often the boundary of the surface. We show that a 4-manifold admits a boundary Lefschetz fibration over the disc degenerating over its boundary if and only if it is diffeomorphic to S 1 ×S 3 #nℂP 2 , #mℂP 2 #nℂP 2 or #m(S 2 ×S 2 ).We conclude that the 4-manifolds S 1 ×S 3 #nℂP 2 , #(2m+1)ℂP 2 #nℂP 2 and #(2m+1)S 2 ×S 2 admit stable generalized complex structures whose type change locus has a single component. |
