Mirror symmetry on K3 surfaces via Fourier-Mukai transform (Q1296250)

In the recent paper of \textit{A. Strominger, S.-T. Yau} and \textit{E. Zaslow} [Nucl. Phys., B 479, No. 1-2, 243-259 (1996; Zbl 0896.14024)], the mirror symmetry on Calabi-Yau threefolds admitting a \(T^3\) fibration is interpreted as \(T\)-duality on the \(T^3\) fibres. Here the authors show that the constructed action of Fourier-Mukai transform on the cohomology ring of an elliptic \(K3\) surface \(X\) reproduces relative \(T\)-duality and provides an infinitesimal isometry of the moduli space of algebraic structures on \(X\); this can be interpreted as mirror symmetry because the quantum cohomology of \(K3\) surfaces is trivial.