On homological mirror symmetry for the complement of a smooth ample divisor in a K3 surface

TL;DR

This paper proposes a conjecture linking the symplectic topology of a K3 surface's divisor complement to algebraic geometry, providing proofs for specific divisor degrees.

Contribution

It introduces a new conjecture on homological mirror symmetry for K3 surface complements and proves it for divisors of degree 2 and 4.

Findings

Conjecture relating symplectic and algebraic geometry in K3 surfaces.

Proof of the conjecture for degree 2 and 4 divisors.

Advances understanding of mirror symmetry in complex surfaces.

Abstract

We introduce a conjecture on homological mirror symmetry relating the symplectic topology of the complement of a smooth ample divisor in a K3 surface to algebraic geometry of type III degenerations, and prove it when the degree of the divisor is either 2 or 4.