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Regular version of the site

Working paper

Mirror symmetry and automorphisms

arXiv. arXiv. arXiv, 2019
Kalashnikov E. G., Chiodo A.
We show that there is an extra dimension to the mirror duality discovered in the early nineties by Greene-Plesser and Berglund-Hübsch. Their duality matches cohomology classes of two Calabi--Yau orbifolds. When both orbifolds are equipped with an automorphism s of the same order, our mirror duality involves the weight of the action of s∗ on cohomology. In particular, it matches the respective s-fixed loci, which are not Calabi-Yau in general. When applied to K3 surfaces with non-symplectic automorphism s of odd prime order, this provides a proof that Berglund-Hübsch mirror symmetry implies K3 lattice mirror symmetry replacing earlier case-by-case treatments.