PIRSA:09050028 Conference

DOI10.48660/09050028

Conference/School: Connections in Geometry and Physics - 2009

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}}
}

Abstract

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.

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