An example of Fourier–Mukai partners of minimal elliptic surfaces

Abstract

Let X and Y be smooth projective varieties over C . We say that X and Y are D-equivalent (or, X is a Fourier-Mukai partner of Y ) if their derived categories of bounded complexes of coherent sheaves are equivalent as triangulated categories. The aim of this short note is to find an example of mutually D-equivalent but not isomorphic relatively minimal elliptic surfaces.