Mirror symmetry for Berglund-Hübsch Milnor fibers

Abstract

We explain how to calculate the Fukaya category of the Milnor fiber of a Berglund-Hübsch invertible polynomial, mostly proving a conjecture of Yankı Lekili and Kazushi Ueda on homological mirror symmetry. As usual, we begin by calculating the "very affine" Fukaya category; afterwards, we deform it, generalizing an earlier calculation of David Nadler. The main step of our calculation may be understood as determining a certain canonical extension of a perverse schober.

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Cited by in corpus (2)

• Local mirror symmetry via SYZ
• Nonexistence of exact Lagrangian tori in affine conic bundles over ${\mathbb{C}}^n$