### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*367*(12), 8933-8974.

**The mori program and non-fano toric homological mirror symmetry.** / Ballard, Matthew; Diemer, Colin; Favero, David; Katzarkov, Ludmil; Kerr, Gabriel.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 367, no. 12, pp. 8933-8974.

}

TY - JOUR

T1 - The mori program and non-fano toric homological mirror symmetry

AU - Ballard, Matthew

AU - Diemer, Colin

AU - Favero, David

AU - Katzarkov, Ludmil

AU - Kerr, Gabriel

PY - 2015/12/1

Y1 - 2015/12/1

N2 - 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 ℙ2 at three infinitesimally near points.

AB - 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 ℙ2 at three infinitesimally near points.

UR - http://www.scopus.com/inward/record.url?scp=84943189586&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84943189586&partnerID=8YFLogxK

M3 - Article

VL - 367

SP - 8933

EP - 8974

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 12

ER -