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A Fourier-Mukai transform for stable bundles on K3 surfaces. (English) Zbl 0872.14013

The authors propose a Fourier-Mukai transform for sheaves on K3 surfaces. Given a K3 surface \(X\), the role of “mirror” K3 surface \(\widehat X\) is played by a suitable surface component of the moduli space of stable sheaves on \(X\). When \(X\) satisfies some conditions one can choose \(\widehat X\), and the universal object on \(X\times \widehat X\), so that the Fourier-Mukai transform is invertible. In this case one can also show that the Fourier-Mukai transform preserves the stability of vector bundles of zero degree.
Reviewer: C.Bartocci

MSC:

14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
18E30 Derived categories, triangulated categories (MSC2010)
14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14J28 \(K3\) surfaces and Enriques surfaces
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