Duke Mathematical Journal

Derived automorphism groups of K3 surfaces of Picard rank 1

Arend Bayer and Tom Bridgeland

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We give a complete description of the group of exact autoequivalences of the bounded derived category of coherent sheaves on a K3 surface of Picard rank 1. We do this by proving that a distinguished connected component of the space of stability conditions is preserved by all autoequivalences and is contractible.

Article information

Duke Math. J., Volume 166, Number 1 (2017), 75-124.

Received: 14 May 2014
Revised: 5 February 2016
First available in Project Euclid: 14 September 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 14J28: $K3$ surfaces and Enriques surfaces 14J33: Mirror symmetry [See also 11G42, 53D37] 18E30: Derived categories, triangulated categories

derived category autoequivalences stability conditions K3 surfaces mirror symmetry


Bayer, Arend; Bridgeland, Tom. Derived automorphism groups of K3 surfaces of Picard rank $1$. Duke Math. J. 166 (2017), no. 1, 75--124. doi:10.1215/00127094-3674332. https://projecteuclid.org/euclid.dmj/1473854468

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