## Duke Mathematical Journal

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

### Derived automorphism groups of K3 surfaces of Picard rank $1$

Arend Bayer and Tom Bridgeland

#### Abstract

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

**Source**

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

**Dates**

Received: 14 May 2014

Revised: 5 February 2016

First available in Project Euclid: 14 September 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.dmj/1473854468

**Digital Object Identifier**

doi:10.1215/00127094-3674332

**Subjects**

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

**Keywords**

derived category autoequivalences stability conditions K3 surfaces mirror symmetry

#### Citation

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