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The Mori program and non-Fano toric homological mirror symmetry. (English) Zbl 1400.14104

The authors provide 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. The paper explores additional connections between Homological Mirror Symmetry and Mori Program in the setting of toric varieties.

MSC:

14J33 Mirror symmetry (algebro-geometric aspects)
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
18E30 Derived categories, triangulated categories (MSC2010)
14T05 Tropical geometry (MSC2010)
14L24 Geometric invariant theory
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
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