Mirror symmetry for Berglund-H\"ubsch Milnor fibers

TL;DR

This paper proves a homological mirror symmetry conjecture by calculating the Fukaya category of Milnor fibers associated with Berglund-H"ubsch invertible polynomials, involving advanced categorical and geometric techniques.

Contribution

It provides a detailed calculation of the Fukaya category for these Milnor fibers and confirms a conjecture relating to homological mirror symmetry.

Findings

Confirmed the homological mirror symmetry conjecture for Berglund-H"ubsch Milnor fibers.

Developed methods to compute the Fukaya category via deformation and perverse schobers.

Extended previous calculations of the Fukaya category to a broader class of polynomials.

Abstract

We explain how to calculate the Fukaya category of the Milnor fiber of a Berglund-H\"ubsch invertible polynomial, mostly proving a conjecture of Yank{\i} 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.