The mori program and non-fano toric homological mirror symmetry

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

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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
Issue number12
StatePublished - Dec 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2015 American Mathematical Society.


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