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Homological mirror symmetry for nodal stacky curves

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>7/07/2025
<mark>Journal</mark>Mathematical Research Letters
Issue number1
Volume32
Number of pages61
Pages (from-to)177-237
Publication StatusPublished
<mark>Original language</mark>English

Abstract

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 [LU22] 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 [LP17] to allow the irreducible components of the curve to have non-trivial generic stabiliser. We then prove that the A-model which results from this strategy is graded symplectomorphic to the corresponding quotient of the Milnor fibre.