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Homological mirror symmetry for invertible polynomials in two variables. (English) Zbl 07507152

Summary: In this paper, we give a proof of homological mirror symmetry for two variable invertible polynomials, where the symmetry group on the B-side is taken to be maximal. The proof involves an explicit gluing construction of the Milnor fibres, and, as an application, we prove derived equivalences between certain nodal stacky curves, some of whose irreducible components have non-trivial generic stabiliser.

MSC:

14F06 Sheaves in algebraic geometry
14H10 Families, moduli of curves (algebraic)
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
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