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arXiv · 2602.04866

Homological mirror symmetry for orbifold log Calabi-Yau surfaces

Bogdan Simeonov
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Abstract

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 $(\mathcal{X},\mathcal{D})$ with $\mathcal{X}$ a projective rational surface with isolated cyclic quotient orbifold points and $\mathcal{D}$ 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.

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Bogdan Simeonov. 2026-02-04. Homological mirror symmetry for orbifold log Calabi-Yau surfaces. https://arxiv.org/abs/2602.04866

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