Lagrangian torus fibrations

Vendredi 1er février 2019 15:30-16:30 - Jonny Evans - UC London

Résumé : (Work in progress, joint with Mirko Mauri, Dmitry Tonkonog, and Renato Vianna) In the early days of mirror symmetry, people expected that Calabi-Yau 3-folds should admit Lagrangian torus fibrations over the 3-sphere such that the discriminant locus (the subset of the 3-sphere over which there are singular fibres) is a trivalent graph. Work of Joyce, Ruan, Castano-Bernard and Matessi showed that this was an unrealistic expectation : generically, you should expect to have codimension 1 discriminant locus (a thickening of the trivalent graph into a ribbon). I will explain how (in the important local model of a « negative vertex ») one can actually find fibrations whose discriminant locus has codimension 2 (as per the original expectation). The way we construct Lagrangian torus fibrations is very simple and very general and I will also use it to write down a Lagrangian torus fibration on the 4-dimensional pair of pants and (by compactifying suitably) on a certain Horikawa surface.

Lieu : salle 3L8

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