On the complex affine structures of SYZ-fibration of del Pezzo surfaces (Q6109926)

The paper proves two results related to mirror symmetry for the non-compact Calabi-Yau surface defined as the complement of a smooth elliptic curve in the complex projective plane. The first result shows that two integral affine manifolds, one coming from the periods of the holomorphic volume form and the other coming from an algebro-geometric degeneration, are actually the same. The second result compares a Floer-theoretic construction of the mirror geometry with an algebro-geometric construction.