The mori program and non-fano toric homological mirror symmetry

Matthew Ballard, Colin Diemer, David Favero, Ludmil Katzarkov, Gabriel Kerr

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 ℙ2 at three infinitesimally near points.

Original languageEnglish (US)
Pages (from-to)8933-8974
Number of pages42
JournalTransactions of the American Mathematical Society
Volume367
Issue number12
StatePublished - Dec 1 2015

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Mirror Symmetry
Mirrors
Toric Varieties
Orthogonal Decomposition
Ginzburg-Landau Model
Pursuit
Decomposition
Blow-up
Bundle
Mirror
Continue
Model

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Transactions of the American Mathematical Society, Vol. 367, No. 12, 01.12.2015, p. 8933-8974.

Research output: Contribution to journalArticle

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, vol. 367, no. 12, pp. 8933-8974.
Ballard, Matthew ; Diemer, Colin ; Favero, David ; Katzarkov, Ludmil ; Kerr, Gabriel. / The mori program and non-fano toric homological mirror symmetry. In: Transactions of the American Mathematical Society. 2015 ; Vol. 367, No. 12. pp. 8933-8974.
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