publications

2026

1. 

   Homological mirror symmetry for orbifold log Calabi-Yau surfaces

   Feb 2026

   arXiv:2602.04866

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   We prove homological mirror symmetry for orbifold log Calabi-Yau surfaces at the large complex structure limit by constructing an abstract Lefschetz fibration associated to each pair (\mathcalX,\mathcalD) with \mathcalX a projective rational surface with isolated cyclic quotient orbifold points and \mathcalD a stacky anticanonical divisor. We describe a Lefschetz stabilization procedure which, on the mirror, corresponds to the special McKay correspondence of Ishii and Ueda arXiv:1104.2381v2 [math.AG]. Moreover, we relate our abstract construction to an explicit Laurent polynomial mirror in an example consisting of a family of orbifold del Pezzo surfaces.

   @misc{simeonov_homological_2026,
     title = {Homological {mirror} {symmetry} for orbifold log {Calabi}-{Yau} surfaces},
     url = {https://arxiv.org/abs/2602.04866},
     doi = {10.48550/arXiv.2602.04866},
     publisher = {arXiv},
     month = feb,
     year = {2026},
     note = {arXiv:2602.04866},
     keywords = {Mathematics - Symplectic Geometry, Mathematics - Algebraic Geometry},
   }