Mirror symmetry and automorphisms

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Mirror symmetry and automorphisms

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.

Language: English

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Keywords: Mirror symmetry

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n this paper, we will introduce Quantum Toric Varieties which are (non-commutative) generalizations of ordinary toric varieties where all the tori of the classical theory are replaced by quantum tori. Quantum toric geometry is the non-commutative version of the classical theory; it generalizes non-trivially most of the theorems and properties of toric geometry. By considering ...

Added: September 24, 2021

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Added: February 3, 2021

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Added: November 18, 2020

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