Kyoto Journal of Mathematics

Perverse coherent sheaves and Fourier–Mukai transforms on surfaces, I

Kōta Yoshioka

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We study perverse coherent sheaves on the resolution of rational double points. As examples, we consider rational double points on 2-dimensional moduli spaces of stable sheaves on K3 and elliptic surfaces. Then we show that perverse coherent sheaves appear in the theory of Fourier–Mukai transforms. As an application, we generalize the Fourier–Mukai duality for K3 surfaces to our situation.

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Kyoto J. Math., Volume 53, Number 2 (2013), 261-344.

First available in Project Euclid: 20 May 2013

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Primary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13}


Yoshioka, Kōta. Perverse coherent sheaves and Fourier–Mukai transforms on surfaces, I. Kyoto J. Math. 53 (2013), no. 2, 261--344. doi:10.1215/21562261-2081234.

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