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 language||English (US)|
|Number of pages||42|
|Journal||Transactions of the American Mathematical Society|
|State||Published - Dec 1 2015|
ASJC Scopus subject areas
- Applied Mathematics