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
N1 - Publisher Copyright:
© 2015 American Mathematical Society.
PY - 2015/12
Y1 - 2015/12
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.
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U2 - 10.1090/S0002-9947-2015-06541-6
DO - 10.1090/S0002-9947-2015-06541-6
M3 - Article
AN - SCOPUS:84943189586
SN - 0002-9947
VL - 367
SP - 8933
EP - 8974
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 12
ER -