Transformation de Fourier-Mukai sur les Surfaces Hyperkählériennes

Details Transformation de Fourier-Mukai sur les Surfaces Hyperkählériennes Transformation de Fourier-Mukai sur les Surfaces Hyperkählériennes

1994-07-15

arxiv.org/abs/dg-ga/9407004v1

Mathematics

Differential Geometry

5 pages (French language), AmsTeX v.2.1 with Amsppt.sty, Preprint DIMA 264/1994

Scientific paper

Given two compact hyperk\"ahler surfaces $X$ and $Y$ and a holomorphic vector bundle $Q$ on $X\times Y$, which is a generalized instanton, one can define a Fourier-Mukai transform, which, under suitable assumptions, maps vector bundles on $X$ to vector bundles on $Y$. If $X$ and $Y$ are dual complex tori, this transform maps instantons on $X$ to instantons on $Y$. After a quick review of these results, we define a Fourier-Mukai transform in the case when $X$ is a K3 surface, and study the behaviour of instantons on $X$ under this transform. Hard copies may be mailed on request

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