An example of Fourier--Mukai partners of minimal elliptic surfaces

Details An example of Fourier--Mukai partners of minimal elliptic surfaces An example of Fourier--Mukai partners of minimal elliptic surfaces

2003-12-30

arxiv.org/abs/math/0312499v2

Mathematics

Algebraic Geometry

Scientific paper

Let $X$ and $Y$ be smooth projective varieties over $\C$. We say that $X$ and $Y$ are \emph{D-equivalent} (or, $X$ is a \emph{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.

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