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

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.

arXiv comment5 pages, 9 figures