Our very own Pranav Chakravarthy will speak in the geometry seminar on 5th May, at 2pm in the Salle des Profs (building NO, Campus de la Plaine). Pranav’s title is “Almost toric fibrations on K3 surfaces” and his abstract is below.
It is known that a manifold diffeomorphic to a K3 surface admits an almost toric fibration (ATF). However, given a specific symplectic form on a K3 surface it is unclear if it admits an almost toric fibration with lagrangian fibres for the given form. In this talk, we prove that when a Kahler K3 surface admits a Type III Kulikov degeneration with a symplectic form taming the complex structure, the symplectic form admits an ATF whose base is the intersection complex of the degenerate fibre. Furthermore, we shall show that a smooth anti-canonical hypersurface in a smooth toric Fano threefold, equipped with a toric Kähler form, admits such a symplectic Kulikov model. This is based on joint work with Yoel Groman.