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PIRSA:09050028

Mirror Symmetry for Blow Ups

APA

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

Denis Auroux University of California, Berkeley

Talk numberPIRSA:09050028
Talk Type Conference

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.