Legendrian fronts for affine varieties

Vendredi 17 mars 2017 15:30-16:30 - Emmy Murphy - MIT

Résumé : Up to symplectomorphism, every complex affine variety can be presented as a Lagrangian handle decomposition. While this is easy to prove, in practice the process from going from an explicit set of polynomials to an explicit Legendrian front projection is not obvious. We would like to be able to do this for a number of reasons : it allows us to compute the wrapped Fukaya category of the variety, it allows us to easily see the diffeomorphism type, it can be used to prove that two varieties are symplectomorphic, and it gives a new method to construct compact exact Lagrangians. We explain a recipe to produce this Legendrian front from a set of polynomials, and explain some applications, such as showing that the Koras-Russel 3-fold is symplectomorphic to C3. This is joint work with R. Casals.

Lieu : Université de Nantes

Legendrian fronts for affine varieties  Version PDF