Some remarks about the FM-partners of K3 surfaces with Picard numbers 1 and 2

Paolo Stellari

Published 2002-05-12, updated 2005-05-25Version 2

In this paper we prove some results about K3 surfaces with Picard number 1 and 2. In particular, we give a new simple proof of a theorem due to Oguiso which shows that, given an integer $N$, there is a K3 surface with Picard number 2 and at least $N$ non-isomorphic FM-partners. We describe also the Mukai vectors of the moduli spaces associated to the Fourier-Mukai partners of K3 surfaces with Picard number 1.