The Mori Program and Non-Fano Toric Homological Mirror Symmetry
Algebraic Geometry
2013-02-05 v1 Symplectic Geometry
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 -model on toric varieties to semi-orthogonal decompositions on the -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 at three infinitesimally near points.
Keywords
Cite
@article{arxiv.1302.0803,
title = {The Mori Program and Non-Fano Toric Homological Mirror Symmetry},
author = {Matthew Ballard and Colin Diemer and David Favero and Ludmil Katzarkov and Gabriel Kerr},
journal= {arXiv preprint arXiv:1302.0803},
year = {2013}
}
Comments
40 pages, uses Tikz, 7 additional figures