## Kyoto Journal of Mathematics

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

Kōta Yoshioka

#### Abstract

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.

#### Article information

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

Dates
First available in Project Euclid: 20 May 2013

https://projecteuclid.org/euclid.kjm/1369071232

Digital Object Identifier
doi:10.1215/21562261-2081234

Mathematical Reviews number (MathSciNet)
MR3079307

Zentralblatt MATH identifier
1274.14022

#### Citation

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. https://projecteuclid.org/euclid.kjm/1369071232

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