Non-uniqueness of Fourier-Mukai kernels

Details Non-uniqueness of Fourier-Mukai kernels Non-uniqueness of Fourier-Mukai kernels

2010-09-28

arxiv.org/abs/1009.5577v2

Mathematics

Algebraic Geometry

12 pages. Minor changes. Final version to appear in Math. Zeit

Scientific paper

We prove that the kernels of Fourier-Mukai functors are not unique in
general. On the other hand we show that the cohomology sheaves of those kernels
are unique. We also discuss several properties of the functor sending an object
in the derived category of the product of two smooth projective schemes to the
corresponding Fourier-Mukai functor.

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