### Abstract

In the case of toric varieties, we continue the pursuit of Kontsevich’s fundamental insight, Homological Mirror Symmetry, by unifying it with the Mori program. We give a refined conjectural version of Homological Mirror Symmetry relating semi-orthogonal decompositions of the B-model on toric varieties to semi-orthogonal decompositions on the A-model on the mirror Landau-Ginzburg models. As evidence, we prove a new case of Homological Mirror Symmetry for a toric surface whose anticanonical bundle is not nef, namely a certain blow-up of ℙ^{2} at three infinitesimally near points.

Original language | English (US) |
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Pages (from-to) | 8933-8974 |

Number of pages | 42 |

Journal | Transactions of the American Mathematical Society |

Volume | 367 |

Issue number | 12 |

State | Published - Dec 1 2015 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Ballard, M., Diemer, C., Favero, D., Katzarkov, L., & Kerr, G. (2015). The mori program and non-fano toric homological mirror symmetry.

*Transactions of the American Mathematical Society*,*367*(12), 8933-8974.