This paper explores homological mirror symmetry for weighted blowups of toric varietes. It will be shown that both the A-model and B-model categories have natural semi-orthogonal decompositions. An explicit equivalence of the right orthogonal categories will be shown for the case of toric surfaces. © 2008.
Kerr, G. (2008). Weighted blowups and mirror symmetry for toric surfaces. Advances in Mathematics, 219(1), 199–250. https://doi.org/10.1016/j.aim.2008.04.005