Mirror Symmetry for Blow Ups


Auroux, D. (2009). Mirror Symmetry for Blow Ups. Perimeter Institute. https://pirsa.org/09050028


Auroux, Denis. Mirror Symmetry for Blow Ups. Perimeter Institute, May. 08, 2009, https://pirsa.org/09050028


          @misc{ pirsa_PIRSA:09050028,
            doi = {10.48660/09050028},
            url = {https://pirsa.org/09050028},
            author = {Auroux, Denis},
            keywords = {},
            language = {en},
            title = {Mirror Symmetry for Blow Ups},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {may},
            note = {PIRSA:09050028 see, \url{https://pirsa.org}}

Denis Auroux University of California System


This talk is a report on joint work with Mohammed Abouzaid and Ludmil Katzarkov about mirror symmetry for blowups, from the perspective of the Strominger-Yau-Zaslow conjecture. Namely, we first describe how to construct a Lagrangian torus fibration on the blowup of a toric variety X along a codimension 2 subvariety S contained in a toric hypersurface. Then we discuss the SYZ mirror and its instanton corrections, to provide an explicit description of the mirror Landau-Ginzburg model (possibly up to higher order corrections to the superpotential). This construction allows one to recover geometrically the predicted mirrors in various interesting settings: pairs of pants, curves of arbitrary genus, etc.