Homological mirror symmetry for nodal stacky curves

Abstract

In this paper, we establish homological mirror symmetry where the A-model is a finite quotient of the Milnor fibre of an invertible curve singularity, proving a conjecture of Lekili and Ueda from arXiv:1806.04345 in this dimension. Our strategy is to view the B--model as a cycle of stacky projective lines and generalise the approach of Lekili and Polishchuk in arXiv:1705.06023 to allow the irreducible components of the curve to have non-trivial generic stabiliser, a result which might also be of independent interest. We then prove that the A--model which results from this strategy is graded symplectomorphic to the corresponding quotient of the Milnor fibre.

27 pages plus appendix, 9 figures. Comments welcome. V4 moved section on root stacks to appendix. To appear in Mathematical Research Letters