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

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

2002-05-12

arxiv.org/abs/math/0205126v2

Geom. Dedic. 108 (2004), 1--13

Mathematics

Algebraic Geometry

LaTeX, 10 pages

Scientific paper

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.

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